Show that if $a\mid b$ then $2^a-1\mid 2^b-1$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
24572
Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.