MathDB

Binomial congruence

Source: IMOC 2023 N5

September 9, 2023

number theory

Problem Statement

Let

p=4k+1

be a prime and let

|x| \leq \frac{p-1}{2}

such that

\binom{2k}{k}\equiv x \pmod p

. Show that

|x| \leq 2\sqrt{p}