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ICMC 2019/20 Round 1, Problem 2

Source: Imperial College Mathematics Competition 2019/20 - Round 1

August 7, 2020
college contestscomplex numbersSumroots of unity

Problem Statement

Find integers aa and bb such that
ab=30(20200)−31(20202)+32(20204)−⋯+31010(20202020).a^b=3^0\binom{2020}{0}-3^1\binom{2020}{2}+3^2\binom{2020}{4}-\cdots+3^{1010}\binom{2020}{2020}.
proposed by the ICMC Problem Committee
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