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Source: 2019 Taiwan TST Round 3

April 2, 2020
number theoryTaiwan

Problem Statement

Given a prime p=8k+1 p = 8k+1 for some integer k k . Let r r be the remainder when (4kk) \binom{4k}{k} is divided by p p . Prove that r \sqrt{r} is not an integer.
Proposed by Evan Chen
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