$2^b-1$ does not divide $2^a+1$,how can I show it?
62982
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
113458
How to factor $a^n - b^n$?
51858
Showing $\gcd(2^m-1,2^n+1)=1$
50940
Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
125707
A simple proof (hopefully) for $2^x \neq 0$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
145558
Prove that $2^n+3^n $ is never a perfect square