Why is $n^2+4$ never divisible by $3$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
112191
How can I show $q^k$ does not divide ${{n}\choose{q}}$ when $q$ is a prime factor of $n$ and $k$ is the largest integer such that $q^k$ divides $n$?
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
21665
why division by zero is not possible
11470
Divisibility of integers
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
46606
Can an integer of the form $4n+3$ written as a sum of two squares?
68068
For any integer n greater than 1, $4^n+n^4$ is never a prime number.
26069
Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
114393
If $a$ is divisible by $4$, then there exist int $b$ and $c$ such that $a = b^2 - c^2$
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
153281
Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.