How to prove this factor of $a^n+b^n$ if $n$ is odd
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
92057
Prove that for every odd integer n, there is a group...
136077
Prove that $x-1$ is a factor of $x^n-1$
77564
How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
114796
Direct proof that the product of odd integers is odd
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
127293
Prove that $(a-b) \mid (a^n-b^n)$
72054
Show that $\deg f$ is even when $n$ is odd.
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
10236
Show that $a^n \mid b^n$ implies $a \mid b$