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Sum of squares with prime

Source: 2018 Korea Winter Program Practice Test 1 #4

January 6, 2018
number theoryprime numbers

Problem Statement

Let p=4k+1p=4k+1 be a prime. SS is a set of all possible residues equal or smaller then 2k2k when 12(2kk)nk\frac{1}{2} \binom{2k}{k} n^k is divided by pp. Show that ∑x∈Sx2=p \sum_{x \in S} x^2 =p
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