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Number TheorySuperchallengeModular Arithmetic

Modular Arithmetic · Superchallenge problem

How many ordered triples (a,b,c)(a, b, c) with a,b,c∈{1,2,…,10}a, b, c \in \{1, 2, \ldots, 10\} make a2+b2+c2a^2 + b^2 + c^2 divisible by 88?