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2015 Algebra #9: Divisible by Large Power

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March 28, 2015
Divisibilityalgebranumber theory

Problem Statement

Let N=302015N=30^{2015}. Find the number of ordered 4-tuples of integers (A,B,C,D)∈{1,2,…,N}4(A,B,C,D)\in\{1,2,\ldots,N\}^4 (not necessarily distinct) such that for every integer nn, An3+Bn2+2Cn+DAn^3+Bn^2+2Cn+D is divisible by NN.
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