prove that $p^2-1$ is divisible by $24$ if $p$ is a prime greater than $3$
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
139230
Prove that for every positive integer, this polynomial is divisible by 24.
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
64453
Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
75733
Divisibility of prime numbers
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
17965
Prove 24 divides $u^3-u$ for all odd natural numbers $u$