Divisibility Proof $8\mid (x^2 - y^2)$ for $x$ and $y$ odd
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
27449
Product of Divisors of some $n$ proof
127293
Prove that $(a-b) \mid (a^n-b^n)$
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
108385
Irreducible factors of $x^8 - x$ in $Z/2Z[x]$
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
52032
Prove that ${n^5 - n}$ is divisible by 5
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
59653
$x^2-y^2=2s$, s cannot be an odd integer
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$