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## HMMT 2015 Algebra #4 본문

HMMT/2015

### HMMT 2015 Algebra #4

수악중독 2015. 3. 15. 13:39

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 $$203$$.