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2015 Algebra #4: Sums Divisible by 203

Source:

March 28, 2015
algebraSequencesDivisibility

Problem Statement

Compute the number of sequences of integers (a1,…,a200)(a_1,\ldots,a_{200}) such that the following conditions hold.
[*] 0≤a1<a2<⋯<a200≤202.0\leq a_1<a_2<\cdots<a_{200}\leq 202. [*] There exists a positive integer NN with the following property: for every index i∈{1,…,200}i\in\{1,\ldots,200\} there exists an index j∈{1,…,200}j\in\{1,\ldots,200\} such that ai+aj−Na_i+a_j-N is divisible by 203203.
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