Finding remainder when $5^{99}$ is divided by $13$

Prove that, if $p$ is an odd prime number, then ${f(p)}=\binom{2p-1}{p-1}-1$ is divisible by $p^2$

Differentiate expressions involving symmetric matrix $\mathbf{D}=\mathrm{diag}(\tau)\Omega\mathrm{diag}(\tau)$ with respect to element of $\tau$

What's the smallest difference in a group?

Proving that $\int_{0}^{1}x^{n-1}(1-x)^n \mathrm dx =\frac{1}{n {2n\choose n}}$

Unbounded operator such that $P^2=P$

Gamma-Distribution-like integral

Riemann Sphere as extended complex plane

Married Couple Probability Question

$ \lim_{n \to \infty} \frac{\sqrt[n]{n*(n+1)...(2n)}}{n}$

Is there non-trivial examples for groups $G$ satisfying $G = \mathrm{Aut}(G)$

Is $W^2-t$ martingale?

Problem with induction proof in textbook.

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