All Questions

Here is an olympiad-level problem on elementary number theory: Let $a$ be an integer and $n$ a positive integer. Prove that \begin{align} \left(a-1\right)^n \cdot n! \mid a^{n-1} \prod_{i=1}^n \left(...

We say two permutations $\pi_1$ and $\pi_2$ in the symmetric group $\mathfrak{S}_n$ are $k$-equivalent, denoted $\pi_1 \sim_k \pi_2$, if one can be determined from the other after a finite number of ...