TR-MO-R1 2017 Problem 20

$\displaystyle\sum_{n=1}^{30} n^{61} \equiv x \left(\bmod 31^2\right)$ ise $x=?$

A) $404$ B) $434$ C) $465$ D) $496$ E) $527$

Official text Turkish Mathematical Olympiad, first round 2017 official paper, page 11. Quoted with source.

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