Proof that if $n^2/r^2 = p$, with $p$ prime, then $n$ is divisible by $p$
106157
Proof of Euclid's lemma using fundamental theorem of arithmetic
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
77193
Verify that R(p,2) = R(2,p) = p, where R is the Ramsey number
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
80365
Prove that $n$ is divisible by $6$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
34588
Number Theory: $p!+p=n^2$, $p$ = prime
127816
Number theory proof mod p
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$