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+
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Extension of irreducibility results on generalized Laguerre polynomials $L_n^{(-n-s-1)}(x)$
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2024
|
Ankita Jindal
Saranya G. Nair
T. N. Shorey
|
|
+
PDF
Chat
|
Extension of Laguerre polynomials with negative arguments II
|
2022
|
T. N. Shorey
Sneh Bala Sinha
|
|
+
PDF
Chat
|
Extension of Laguerre polynomials with negative arguments
|
2022
|
T. N. Shorey
Sneh Bala Sinha
|
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+
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Extension of Irreducibility results on Generalised Laguerre Polynomials $L_n^{(-1-n-s)}(x)$
|
2022
|
Saranya G Nair
T. N. Shorey
|
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+
PDF
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On the Galois group of Generalised Laguerre polynomials II
|
2020
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
|
+
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The Dirichlet Series and the Dirichlet Theorem on Primes in Arithmetic Progressions
|
2020
|
T. N. Shorey
|
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+
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The Prime Number Theorem with an Error Term
|
2020
|
T. N. Shorey
|
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+
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The Riemann Zeta Function and the Prime Number Theorem
|
2020
|
T. N. Shorey
|
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+
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The Picard Theorems
|
2020
|
T. N. Shorey
|
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+
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Complex Analysis with Applications to Number Theory
|
2020
|
T. N. Shorey
|
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+
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Conformal Mappings and the Riemann Mapping Theorem
|
2020
|
T. N. Shorey
|
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+
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The Cauchy Theorems and Their Applications
|
2020
|
T. N. Shorey
|
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+
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Introduction and Simply Connected Regions
|
2020
|
T. N. Shorey
|
|
+
PDF
Chat
|
Irreducibility of extensions of Laguerre polynomials
|
2019
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
|
+
PDF
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On Baker's explicit $abc$-conjecture
|
2019
|
Kwok Chi Chim
T. N. Shorey
Sneh Bala Sinha
|
|
+
PDF
|
Explicit abc-conjecture and its applications
|
2019
|
Kwok Chi Chim
Saranya G. Nair
T. N. Shorey
|
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+
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Irreducibility of extensions of Laguerre Polynomials
|
2019
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
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+
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On the Galois group of Generalised Laguerre polynomials II
|
2019
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
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+
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On the Galois group of Generalised Laguerre polynomials II
|
2019
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
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+
|
Irreducibility of extensions of Laguerre Polynomials
|
2019
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
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+
|
On products from blocks of consecutive odd integers
|
2018
|
Saranya G. Nair
T. N. Shorey
|
|
+
|
Irreducibility of generalized Laguerre polynomials $L_n^{(1/2+u)}(x^2)$ with $-18 \leq u \leq -2$
|
2018
|
Saranya G. Nair
T. N. Shorey
|
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+
|
Irreducibility of generalized Hermite–Laguerre polynomials III
|
2016
|
Shanta Laishram
T. N. Shorey
|
|
+
|
Arithmetic Properties of Blocks of Consecutive Integers
|
2016
|
T. N. Shorey
R. Tijdeman
|
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+
|
On the equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi><mml:mi>!</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>!</mml:mi><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>!</mml:mi><mml:mo>⋯</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t…
|
2015
|
Saranya G. Nair
T. N. Shorey
|
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+
|
Erratum to “Irreducibility of Laguerre Polynomial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><…
|
2015
|
Saranya G. Nair
T. N. Shorey
|
|
+
|
Irreducibility of generalized Laguerre polynomials<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo …
|
2015
|
Shanta Laishram
Saranya G. Nair
T. N. Shorey
|
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+
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Lower bounds for the greatest prime factor of product of consecutive positive integers
|
2015
|
Saranya G. Nair
T. N. Shorey
|
|
+
|
Irreducibility of Laguerre Polynomial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:…
|
2015
|
Saranya G. Nair
T. N. Shorey
|
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+
|
Squares and factorials in products of factorials
|
2014
|
Florian Luca
N. Saradha
T. N. Shorey
|
|
+
|
Squares in blocks from an arithmetic progression and Galois group of Laguerre polynomials
|
2014
|
N. Saradha
T. N. Shorey
|
|
+
|
Some Methods of Erdős Applied to Finite Arithmetic Progressions
|
2013
|
T. N. Shorey
Robert Tijdeman
|
|
+
PDF
|
Irreducibility of generalized Hermite-Laguerre polynomials
|
2012
|
Shanta Laishram
T. N. Shorey
|
|
+
|
On the greatest prime factors of an arithmetical progression (III)
|
2012
|
T. N. Shorey
Robert Tijdeman
|
|
+
|
On the greatest prime factor of an arithmetical progression
|
2012
|
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
Baker's explicit abc-conjecture and applications
|
2012
|
Shanta Laishram
T. N. Shorey
|
|
+
PDF
Chat
|
Extensions of Schur’s irreducibility results
|
2011
|
Shanta Laishram
T. N. Shorey
|
|
+
|
Baker's Explicit abc-Conjecture and applications
|
2011
|
Shanta Laishram
T. N. Shorey
|
|
+
PDF
|
Generalizations of some irreducibility results by Schur
|
2010
|
T. N. Shorey
R. Tijdeman
|
|
+
|
Products of Fibonacci numbers with indices in an interval and at most four omitted being a power
|
2009
|
Florian Luca
T. N. Shorey
|
|
+
|
Irreducibility of generalized Hermite-Laguerre Polynomials II
|
2009
|
Shanta Laishram
T. N. Shorey
|
|
+
|
The number of prime divisors of consecutive integers
|
2009
|
R. Balasubramanian
Shanta Laishram
T. N. Shorey
R. Thangadurai
|
|
+
PDF
|
Divisibility properties of generalized Laguerre polynomials
|
2009
|
Clemens Fuchs
T. N. Shorey
|
|
+
|
THE NUMBER OF PRIME DIVISORS OF A PRODUCT
|
2009
|
R. Balasubramanian
Shanta Laishram
T. N. Shorey
R. Thangadurai
|
|
+
|
Almost perfect powers in consecutive integers (II)
|
2008
|
N. Saradha
T. N. Shorey
|
|
+
|
Products of members of Lucas sequences with indices in an interval being a power
|
2008
|
Florian Luca
T. N. Shorey
|
|
+
PDF
|
Diophantine equations with products of consecutive terms in Lucas sequences II
|
2008
|
Florian Luca
T. N. Shorey
|
|
+
PDF
|
Squares in arithmetic progression with at most two terms omitted
|
2008
|
Shanta Laishram
T. N. Shorey
|
|
+
PDF
|
Squares in products in arithmetic progression with at most one term omitted and common difference a prime power
|
2008
|
Shanta Laishram
T. N. Shorey
Szabolcs Tengely
|
|
+
PDF
|
An extension of a theorem of Euler
|
2007
|
Noriko Hirata-Kohno
Shanta Laishram
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
On the equation n(n+d)⋅⋅⋅(n+(i<sub>0</sub>-1)d)(n+(i<sub>0</sub>+1)d)⋅⋅⋅(n+(k-1)d)=y<sup>l</sup>with 0<i<sub>0</sub><k-1
|
2007
|
N. Saradha
T. N. Shorey
|
|
+
|
The greatest prime divisor of a product of terms in an arithmetic progression
|
2006
|
Shanta Laishram
T. N. Shorey
|
|
+
|
GRIMM'S CONJECTURE ON CONSECUTIVE INTEGERS
|
2006
|
Shanta Laishram
T. N. Shorey
|
|
+
PDF
|
Contributions towards a conjecture of Erdos on perfect powers in arithmetic progression
|
2005
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
The greatest prime divisor of a product of consecutive integers
|
2005
|
Shanta Laishram
T. N. Shorey
|
|
+
|
Diophantine equations with products of consecutive terms in Lucas sequences
|
2004
|
Florian Luca
T. N. Shorey
|
|
+
|
Number of prime divisors in a product of terms of an arithmetic progression
|
2004
|
Shanta Laishram
T. N. Shorey
|
|
+
|
Almost squares in arithmetic progression (III)
|
2004
|
Anirban Mukhopadhyay
T. N. Shorey
|
|
+
PDF
|
Number of prime divisors in a product of consecutive integers
|
2004
|
Shanta Laishram
T. N. Shorey
|
|
+
|
under the guidance of
|
2004
|
Shanta Laishram
T. N. Shorey
|
|
+
PDF
|
None
|
2003
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
None
|
2003
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
Almost squares in arithmetic progression (II)
|
2003
|
Anirban Mukhopadhyay
T. N. Shorey
|
|
+
|
Approximations of Algebraic Numbers by Rationals: A Theorem of Thue
|
2003
|
T. N. Shorey
|
|
+
PDF
|
On the Diophantine equation (x<sup>m</sup>-1)/(x-1) = (y<sup>n</sup>-1)/(y-1)
|
2002
|
Yann Bugeaud
T. N. Shorey
|
|
+
|
Powers in Arithmetic Progression
|
2002
|
T. N. Shorey
|
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+
|
A Panorama of Number Theory <i>or</i> The View from Baker's Garden
|
2002
|
Gisbert Wüstholz
Gisbert Wüstholz
Gisbert Wüstholz
Kunrui Yu
Sinnou David
Kálmán Győry
Yuri Bilu
Paula B. Cohen
Jürgen Wolfart
Peter Sarnak
|
|
+
|
Powers in arithmetic progressions (II) (New Aspects of Analytic Number Theory)
|
2002
|
T. N. Shorey
|
|
+
PDF
|
Some extensions and refinements of a theorem of Sylvester
|
2002
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
|
+
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On the Diophantine equation (x m −1)/(x−1) = (y n −1)/(y−1)
|
2002
|
Yann Bugeaud
T. N. Shorey
|
|
+
|
DIOPHANTINE APPROXIMATION ON LINEAR ALGEBRAIC GROUPS: TRANSCENDENCE PROPERTIES OF THE EXPONENTIAL FUNCTION IN SEVERAL VARIABLES (Grundlehren der Mathematischen Wissenschaften 326) <i>By</i> M<scp>ICHEL</scp> W<scp>ALDSCHMIDT</scp>: 633 pp., $58.50, <scp>ISBN</scp> 3-540-66785-7 (Springer, Berlin, 2000).
|
2002
|
T. N. Shorey
|
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+
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An Equation of Goormaghtigh and Diophantine Approximations
|
2002
|
T. N. Shorey
|
|
+
|
On the number of solutions of the generalized Ramanujan-Nagell equation
|
2001
|
Yann Bugeaud
T. N. Shorey
|
|
+
PDF
|
Almost perfect powers in consecutive integers
|
2001
|
Guillaume Hanrot
N. Saradha
T. N. Shorey
|
|
+
PDF
|
Almost perfect powers in arithmetic progression
|
2001
|
N. Saradha
T. N. Shorey
|
|
+
|
Transcendental infinite sums
|
2001
|
Sukumar Das Adhikari
N. Saradha
T. N. Shorey
R. Tijdeman
|
|
+
|
Exponential Diophantine Equations Involving Products of Consecutive Integers and Related Equations
|
2000
|
T. N. Shorey
|
|
+
|
Exponential Diophantine Equations Involving Products of Consecutive Integers and Related Equations
|
2000
|
T. N. Shorey
|
|
+
|
Irreducibility of polynomials and arithmetic progressions with equal products of terms
|
1999
|
Frits Beukers
T. N. Shorey
R. Tijdeman
|
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+
|
The equation formula here has no solution with x square
|
1999
|
Yann Bugeaud
Max Mignotte
Y. Arun Roy
T. N. Shorey
|
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+
|
The equation <i>x</i><sup><i>n</i></sup>−1/<i>x</i>−1= <i>y</i><sup><i>q</i></sup> with <i>x</i> square
|
1999
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
On an equation of Goormaghtigh
|
1998
|
Yu. V. Nesterenko
T. N. Shorey
|
|
+
|
Perfect powers in products of terms in an arithmetical progression. IV
|
1998
|
R. Balasubramanian
T. N. Shorey
|
|
+
PDF
|
Corrections to the paper "On values of a polynomial a arithmetic progressions with equal products" (Acta Arith. 72 (1995), 67-76)
|
1998
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
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+
|
Analytic Number Theory
|
1997
|
Yoichi Motohashi
Yoichi Motohashi
Enrico Bombieri
Enrico Bombieri
Enrico Bombieri
Jörg Brüdern
Jan‐Hendrik Evertse
John Friedlander
Andrew Granville
Adolf Hildebrand
|
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+
|
On the Equation (<i>x</i><sup> <i>m</i> </sup> – 1)/(<i>x</i> – 1) = <i>y</i><sup> <i>q</i> </sup> with <i>x</i> Power
|
1997
|
Noriko Hirata-Kohno
T. N. Shorey
|
|
+
|
Some Methods of Erdôs Applied to Finite Arithmetic Progressions
|
1997
|
T. N. Shorey
R. Tijdeman
|
|
+
|
Perfect powers in products of arithmetical progressions with fixed initial term
|
1996
|
T. N. Shorey
|
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+
|
On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors
|
1996
|
R. Balasubramanian
M. Langevin
T. N. Shorey
Michel Waldschmidt
|
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+
|
The equations (x + 1) … (x + k) = (y + 1) … (y + mk), m = 5,6
|
1996
|
Max Mignotte
T. N. Shorey
|
|
+
PDF
|
Perfect powers in products of integers from a block of consecutive integers (II)
|
1996
|
T. N. Shorey
Yu. V. Nesterenko
|
|
+
|
On a conjecture that a product of <i>k</i> consecutive positive integers is never equal to a product of <i>mk</i> consecutive positive integers except for 8.9.10 = 6!
|
1995
|
T. N. Shorey
|
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+
|
On arithmetic progressions of equal lengths with equal products
|
1995
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
On values of a polynomial at arithmetic progressions with equal products
|
1995
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2
|
1995
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
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+
|
Applications of Baker's theory of linear forms in logarithms to exponential diophantine equations(Analytic Number Theory)
|
1994
|
T. N. Shorey
|
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+
PDF
|
On the equationx(x +d 1)…(x + (k - 1)d 1) =y(y +d 2)…(y + (mk - 1)d 2)
|
1994
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
On arithmetic progressions with equal products
|
1994
|
N. Saradha
T. N. Shorey
R. Tijdeman
|
|
+
|
On the equation f(x + 1)...f(x + k)=f(y + 1)...f(y + mk)
|
1993
|
R. Balasubramanian
T. N. Shorey
|
|
+
PDF
|
Squares in products from a block of consecutive integers
|
1993
|
R. Balasubramanian
T. N. Shorey
|
|
+
|
On the equation (x+1)...(x+k) = (y+1)...(y+mk)
|
1992
|
N. Saradha
T. N. Shorey
|
|
+
PDF
|
Perfect powers in products of terms in an arithmetical progression III
|
1992
|
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
On the number of prime factors of a finite arithmetical progression
|
1992
|
T. N. Shorey
R. Tijdeman
|
|
+
|
On the equation x(x + d) ... (x + (k – 1)d) = y(y + d) ... (y + (mk – 1)d)
|
1992
|
N. Saradha
T. N. Shorey
|
|
+
|
Perfect powers in arithmetical progression (II)
|
1992
|
T. N. Shorey
R. Tijdeman
|
|
+
|
The equations (x+1)…(x+k)=(y+1)…(y+mk) with m=3,4
|
1991
|
N. Saradha
T. N. Shorey
|
|
+
|
On the ratio of two blocks of consecutive integers
|
1990
|
N. Saradha
T. N. Shorey
|
|
+
|
Perfect powers in products of terms in an arithmetical progression (II)
|
1990
|
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
On the greatest prime factor of an arithmetical progression. II
|
1990
|
T. N. Shorey
R. Tijdeman
|
|
+
|
On the maximal length of two sequences of consecutive integers with the same prime divisors
|
1989
|
R. Balasubramanian
T. N. Shorey
Michel Waldschmidt
|
|
+
PDF
|
Integers with identical digits
|
1989
|
T. N. Shorey
|
|
+
|
Some exponential Diophantine equations
|
1988
|
T. N. Shorey
|
|
+
|
On the denominators of equivalent algebraic numbers
|
1988
|
Kálmán Győry
T. N. Shorey
|
|
+
|
Pure powers in recurrence sequences and some related diophantine equations
|
1987
|
T. N. Shorey
C. L. Stewart
|
|
+
|
Metrical Results on Square Free Divisors of Convergents of Continued Fractions
|
1987
|
T. N. Shorey
Srimeenakshi Srinivasan
|
|
+
PDF
|
Equal values of binary forms at integral points
|
1987
|
Jan‐Hendrik Evertse
Kálmán Győry
T. N. Shorey
R. Tijdeman
|
|
+
PDF
|
Odd values of the Ramanujan $\tau$-function
|
1987
|
M. Ram Murty
V. Kumar Murty
T. N. Shorey
|
|
+
PDF
|
Perfect powers in products of integers from a block of consecutive integers
|
1987
|
T. N. Shorey
|
|
+
|
Results from algebraic number theory
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
Exponential Diophantine Equations
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
The Thue–Mahler equation
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
The Catalan equation and related equations
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
The superelliptic equation
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
Binary recurrence sequences with rational roots
|
1986
|
T. N. Shorey
R. Tijdeman
|
|
+
|
Estimates of linear forms in logarithms
|
1986
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T. N. Shorey
R. Tijdeman
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+
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The Fermat equation
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1986
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T. N. Shorey
R. Tijdeman
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+
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The generalised superelliptic equation
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1986
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T. N. Shorey
R. Tijdeman
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+
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Purely exponential equations
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1986
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T. N. Shorey
R. Tijdeman
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+
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Perfect powers at integral values of a polynomial
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1986
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T. N. Shorey
R. Tijdeman
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+
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Diophantine equations and recurrence sequences
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1986
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T. N. Shorey
R. Tijdeman
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+
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Perfect powers in values of certain polynomials at integer points
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1986
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T. N. Shorey
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+
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On the equation zq=(xn−1)/(x−1)
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1986
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T. N. Shorey
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+
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On the equation axm − byn = k
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1986
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T. N. Shorey
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+
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On the ratio of values of a polynomial
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1984
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T. N. Shorey
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+
PDF
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On the equation $a(x^m-1)/(x-1)=b(y^n-1)/(y-1)$: II
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1984
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T. N. Shorey
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+
PDF
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On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
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1983
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T. N. Shorey
C. L. Stewart
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+
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Divisors of convergents of a continued fraction
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1983
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T. N. Shorey
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+
PDF
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The equation $ax^m + by^m = cx^n + dy^n$
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1982
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T. N. Shorey
|
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+
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On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers, II
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1981
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T. N. Shorey
C. L. Stewart
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+
PDF
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On the equation $a(x^m-1)/(x-1)=b(y^n-1)/(y-1)$.
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1980
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R. Balasubramanian
T. N. Shorey
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+
PDF
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On the greatest prime factor of $(ax^m + by^n)$
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1980
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T. N. Shorey
|
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+
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Lectures on irregularities of distribution
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1977
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Wolfgang M. Schmidt
T. N. Shorey
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+
PDF
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New applications of Diophantine approximations to Diophantine equations.
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1976
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T. N. Shorey
R. Tijdeman
|
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+
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Some applications of linear forms in logarithms
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1976
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T. N. Shorey
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+
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On the greatest prime factors of polynomials at integer points
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1976
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T. N. Shorey
R. Tijdeman
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+
PDF
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On the greatest prime factor of $2^p - 1$ for a prime p and other expressions
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1976
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P. Erdős
T. N. Shorey
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+
PDF
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On linear forms in the logarithms of algebraic numbers
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1976
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T. N. Shorey
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+
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Linear Forms in the Logarithms of Algebraic Numbers with Small Coefficients II
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1974
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T. N. Shorey
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+
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On the sum ∑k=13 | 2πk − αk |, αk algebraic numbers
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1974
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T. N. Shorey
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+
PDF
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On gaps between numbers with a large prime factor. II
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1974
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T. N. Shorey
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+
PDF
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On gaps between numbers with a large prime factor
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1973
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K. Ramachandra
T. N. Shorey
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+
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P-Adic analogue of a theorem of Tijdeman and its application
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1972
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T. N. Shorey
|
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+
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Algebraic independence of certain numbers in the p-adic domain
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1972
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T. N. Shorey
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