Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
3109
Prove that $(p+q)^m \leq p^m+q^m$
112120
Find all primes of the form $2^{2^n} + 5$ for a nonnegative integer n
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
118574
prove that $24 \mid a(a^2-1)$
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
88838
How can I prove this inequality for $n\geq 2$?
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
54359
Odd Primes Problem Proof
148713
If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $