Hello, I have a problem need to solve:
S(n) = 1^k + 2^k +..+n^k
input: n<=10^9, k<=40
output: S(n)%(10^9+7).
One more issue:
how to calculate ((n^k)/x)%p which very big n and k.
Thank for helping me.
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Время на сервере: 24.08.2024 13:09:37 (j2).
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See here for finding S(n). ((n^k)/x)%p = ((n^k)%(x*p))/x. Use binary exponentiation to evaluate (n^k)%(x*p).
Thanks you
Easy to prove that the answer is a polynomial with deg ≤ k + 1. So you can find its coefficients using Gaussian elimination or any other way to interpolate it.
Easy to prove that the answer is a polynomial with deg ≤ k + 1.
how?
For instance, using recurrent equation for sum of k-th powers through previous powers sums (see the link above).
Check Div1-500 here.