Given $y,n\in\mathbb{N}$ and knowing the value $y^n$, is there an efficient way to calculate $(y+1)^n$? Anything faster than the binomial theorem is welcome.
2026-03-25 12:45:45.1774442745
Efficient algorithm: $(y+1)^n$
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I believe, that the knowledge of $y^n$ cannot speed up $O(\log n)$ algorithm of exponentiation by squaring. Binomial theorem will give you $O(n)$ at best.