MathDB

p^2 divides $ k(k + 1)(k + 2) ... (k + p - 3) - 1

Source: 2015 Saudi Arabia GMO TST I p4

July 26, 2020

number theorydividesdivisible

Problem Statement

Let

p

be an odd prime number. Prove that there exists a unique integer

k

such that

0 \le k \le p^2

and

p^2

divides

k(k + 1)(k + 2) ... (k + p - 3) - 1

.
Malik Talbi