how to prove if $m^{2}|n^{2}$ then m|n just hint please.
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
55266
Prove that $(n+1)^{n-1}<n^n$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
67527
Proof by Induction that $3^n ≥ 1+2^n$
79847
proving of inequality $(n!)^2 \leq n^n\cdot n!\leq (2n!)$, where $n\in \mathbb{N}$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
49166
$R^n \cong R^m$ iff $n=m$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$