Binomial Coefficients modulo \(2017\)

Algebra Level 4

Given that \(\displaystyle \sum_{n = 0}^{62} {2014 \choose n} \pmod {2017}\) can be written in the form \(a^2\) where \(a\) is a positive integer, find \(a\).

\(2017\) is prime.

This is from the AMC 12B given yesterday.

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