MathDB

21

Part of 2004 Iran MO (3rd Round)

Problems(1)

p|a_1^k + ... + a_n^k for infinitely many p

Source: Iranian National Olympiad (3rd Round) 2004

1/9/2009
a1,a2,…,an a_1, a_2, \ldots, a_n are integers, not all equal. Prove that there exist infinitely many prime numbers p p such that for some k k p\mid a_1^k \plus{} \dots \plus{} a_n^k.
number theorygreatest common divisormodular arithmeticprime numbersnumber theory proposed