On the smallest simultaneous power nonresidue modulo a prime
On the smallest simultaneous power nonresidue modulo a prime
Abstract Let p be a prime and let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>p</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:mi>…</m:mi> <m:mo>,</m:mo> <m:msub> <m:mi>p</m:mi> <m:mi>r</m:mi> </m:msub> </m:mrow> </m:math> ${p_{1},\ldots,p_{r}}$ be distinct prime divisors of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>p</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> ${p-1}$ . We prove that the smallest positive integer n which is …