Reach for the Summit - M-S4-A3

Algebra Level 4

Find the value of:

( ( ∑ k = 0 1010 ( − 1 ) k ( 2020 2 k ) ) 2 + ( ∑ k = 0 1009 ( − 1 ) k ( 2020 2 k + 1 ) ) 2 ) m o d 998244353 \left(\left(\sum_{k=0}^{1010} (-1)^k {2020 \choose 2k} \right)^2 + \left(\sum_{k=0}^{1009} (-1)^k {2020 \choose 2k+1} \right)^2 \right) \bmod 998244353

Reach for the Summit problem set - Mathematics


The answer is 822387450.

Alice Smith by Alice Smith , 20, China

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