HMMT 2015 Algebra #4

Compute the number of sequences of integers \((a_1, \; \cdots ,\; a_{200})\) such taht th following conditions hold.

• \(0 \le a_1 < a_2 < \cdots < a_{200} \le 202\).
  

• There exists a positive integer \(N\) with the following property: for every index \(i \in \{ 1, \; \cdots ,\; 200 \}\) there exists an index \( j \in \{1, \; \cdots ,\; 200\}\) such that \(a_i +a_j -N\) is divisible by \(203\).

정답 \(20503\)