prove that $3$ does not divide $n^2+1$
69902
$3$ never divides $n^2+1$
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
46102
Prove that $2^n +1$ in never a perfect cube
102980
finding all numbers $a,b$ that divide $c$ but product of $a$ and $b$ does not divide $c$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
145558
Prove that $2^n+3^n $ is never a perfect square
122386
How do I prove that $3$ divides $14^{2n}-1$ by induction?
96737
Geometric proof that a Pythagorean triple has a number divisible by $3$?
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
49080
$t^3$ is never equal to