Prove that $ a^6 = b^{11} $
40274
If $|a| = 12, |b| = 22$ and $\langle a \rangle\cap \langle b\rangle \ne e$, prove that $a^6 = b^{11}$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
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
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
71880
Prove that every prime factor of $12x^2+1$ has the form $6n+1$
142263
Assuming $ab^2 = b^3a$ and $a^2=1$ prove that the order of $b$ is $5$.
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
119152
Proving irreducibility of $x^6-72$
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
158807
Proving a fact: $\tan(6^{\circ}) \tan(42^{\circ})= \tan(12^{\circ})\tan(24^{\circ})$
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
80365
Prove that $n$ is divisible by $6$
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$