If $3|(a^2 + b^2)$, show that $3|a$ and $3|b$.
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
62556
Prove $3|n(n+1)(n+2)$ by induction
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
96217
If a and b are non-negative real numbers then demonstrate inequality
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
80095
Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
81618
Prove $||a|-|b| | \leq |a-b|$
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.