Number theory: Which (n,k) pairs satisfy the equation
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
94407
Number of solutions for $x[1] + x[2] + \ldots + x[n] =k$
96861
How find all ordered pairs $(m,n)$ such $\frac{n^3-1}{mn-1}$ is an integer
107964
Simple combinatorics problem.
153647
Elementary number theory and quadratic
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
14783
A Number Theory problem (GCD)
110569
Does anyone know a closed-form expression for a bijection between $\mathbb{N}^k$ and $\mathbb{N}$?
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
136856
Diophantine equation with a prime number
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
65757
Prove that $n! + k$ is a composite number
66216
Squares, Cubes and Prime numbers