MathDB

neither of a^{p−1} - 1 & (a + 1)^{p−1}-1 is divisible p^2

Source: 13-th Hungary-Israel Binational Mathematical Competition 2002

April 7, 2007

number theory unsolvednumber theory

Problem Statement

Let

p \geq 5

be a prime number. Prove that there exists a positive integer

a < p-1

such that neither of

a^{p-1}-1

and

(a+1)^{p-1}-1

is divisible by

p^{2}