Show $(2^m-1,2^n+1)=1$ if $m$ is odd
51858
Showing $\gcd(2^m-1,2^n+1)=1$
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
92166
Number of odd binomial coefficients is a power of $2$
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
100361
Show that ord$_{p}2 = 2^{n + 1}$.
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$