MathDB

n | (p - 1) & p | (n^6 - 1) prove p-n or p+n square

Source: JBMO Shortlist 2007 N3

October 14, 2017

Perfect SquareJBMOnumber theory

Problem Statement

Let

n > 1

be a positive integer and

p

a prime number such that

n | (p - 1)

and

p | (n^6 - 1)

. Prove that at least one of the numbers

p- n

and

p + n

is a perfect square.