All Questions

Let $k$ be a nonnegative integer, how to compute $\prod\limits_{i=1}^{n} A_i$ quickly and accurately, where $$A_i=\begin{bmatrix} 0 & 1\\ i^k & 1 \end{bmatrix}?$$ I know if $k=0$, we can use ...

Let $T(n, k)$ be A107670 (i.e., matrix square of triangle A107667). Here we define the triangular matrix $P$ by $P(n, k) = \frac{(n+1)^{2(n-k)}}{(n-k)!}$ for $0 \leqslant k \leqslant n$ and the ...

I'm interested in a few problems that are related enough that I decided to put them all in one question. What are the fastest known algorithms for finding large Fibonacci numbers modulo $p^k$, and ...