The Number of Solutions of φ (x) = m

Kevin Ford

Type: Article

Publication Date: 1999-07-01

Citations: 57

DOI: https://doi.org/10.2307/121103

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Locations

Annals of Mathematics - View

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+ PDF Chat	Division polynomials and intersection of projective torsion points	2016	Fedor Bogomolov Hang Fu
+	On the equations ϕ(n) = ϕ(n + k) and ϕ(p − 1) = ϕ(q − 1)	2020	Sungjin Kim
+	Popular subsets for Euler’s $$\varphi $$-function	2019	Paul Pollack
+	The Resolved and Unresolved Conjectures of R.D. Carmichael	2017	Brian D. Beasley
+	Wie kann man Primzahlen erkennen?	2006
+	On quotients of values of Euler's function on the Catalan numbers	2016	Bojan Bašić
+ PDF Chat	Values of the Euler Function in Various Sequences	2005	William D. Banks Kevin Ford Florian Luca Francesco Pappalardi Igor E. Shparlinski
+ PDF Chat	Discrete bilinear Radon transforms along arithmetic functions with many common values	2017	Dong Dong Xianchang Meng
+ PDF Chat	Coincidences in the values of the Euler and Carmichael functions	2006	William D. Banks John Friedlander Florian Luca Francesco Pappalardi Igor E. Shparlinski
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Works Cited by This (11)

Action	Title	Year	Authors
+	ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES	1973	Chen Jing-Run
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld
+	Multiplicative Number Theory	1980	H. Davenport
+ PDF Chat	Remarks on the paper "Sur certaines hypothèses concernant les nombres premiers"	1961	Andrzej Schinzel
+	None	1998	Kevin Ford
+ PDF Chat	On Euler’s 𝜙-function	1907	R. D. Carmichael
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős
+ PDF Chat	Note on Euler’s 𝜑-function	1922	R. D. Carmichael
+	On the Distribution of Quadratic Residues (mod <i>p</i> )	1931	H. Davenport
+ PDF Chat	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum