Prove if $7\mid a^2+b^2 \longrightarrow 7\mid a$ and $ 7\mid b$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
89175
Proof of $(a+b)^{n+1}$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
39953
$a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
113789
Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$, find $a_7+a_6+a_5+a_4+...+a_1+a_0$
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
118467
Prove that $a^2+ab+b^2\ge 0$
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
80421
Show that $a - b \mid f(a) - f(b)$