MathDB

N5

Part of 2023-IMOC

Problems(1)

Binomial congruence

Source: IMOC 2023 N5

9/9/2023
Let p=4k+1p=4k+1 be a prime and let ∣x∣≤p−12|x| \leq \frac{p-1}{2} such that (2kk)≡x(modp)\binom{2k}{k}\equiv x \pmod p. Show that ∣x∣≤2p|x| \leq 2\sqrt{p}.
number theory