Show that if $p$ is a prime number $> 3$ then $24 \mid p^2-1$
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
83407
How to show that that $q \mid p-1$?
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
48691
Product of all prime numbers upto some prime $p$
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
46820
If $p$ is a prime such that $p≡1\pmod 7$ then $p ≡1\pmod{14}$
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
54547
Prove this number must be a prime number or 1.