Show that for all prime numbers $p$ greater than $3$, $24$ divides $p^2-1$ evenly.
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
118538
Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
151692
When does $2^n-1$ divide $3^n-1$?
80907
Primes dividing a polynomial
16407
$24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement.
55437
When does $2^{n}$ divide $3^{n}-1$
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
77430
Prove that every prime larger than $3$ gives a remainder of $1$ or $5$ if divided by $6$
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
131488
Show that $p^3+4$ is prime
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$