Proving that if $a^n+b^n \mid a^m+b^m$, then $n \mid m$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
48655
Find all n such that : $3 \mid (n2^{n}+1)$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$