MathDB

p>5 prime, then p-x^2 | p-y^2

Source: Balkan MO 1996, Problem 2

August 16, 2005

floor functionnumber theorynumber theory proposed

Problem Statement

Let

p

be a prime number with

p>5

. Consider the set X \equal{} \left\{p \minus{} n^2 \mid n\in \mathbb{N} ,\ n^2 < p\right\}. Prove that the set

X

has two distinct elements

x

and

y

such that

x\neq 1

and

x\mid y

. Albania