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 $20503$