Prove that if $3|(a^2+b^2)$, then $3|a$ and $3|b$, where $a, b$ are integers
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
80009
Prove that $| |a|-|b| | \le |a-b|$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
81618
Prove $||a|-|b| | \leq |a-b|$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
111267
Prove that: $2^a+3^b<3a+4b$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.