Find all nonnegative integers $m$ and $n$ such that $m!+1=n^2$.
19588
$n!+1$ being a perfect square
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
8609
Prove by induction that $n!>2^n$
124782
Hint for $(n!+1,(n+1)!)$, stuck at $ (n!+1,n+1)$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
45914
Proving that $n!≤((n+1)/2)^n$ by induction
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
106030
Find all the positive integer
155363
Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
32544
Give an example of three positive integers m, n, and r
65763
Number of ways to write n as a sum of k nonnegative integers
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
124456
Given $x \in \mathbb{R}$ and $N \in \mathbb{N}, N>1,$ find integers $h,k$ with $0 < k \leq N $ that satisfy $\lvert{kx - h\rvert} < 1/N.$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
59535
Prove that there exists such a set of $n$ positive integers