If $a^{m}=b^{m}$ and $a^{n}=b^{n}$, show that a=b
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$