Find all solutions to $m^2 − n^2 = 105$, for which both m and n are integers

Question

Can I get a little help for this question?

Find all the integer solutions to $m^2 − n^2 = 105$.

Answer 1

$(m+n)(m-n) = 105$

$(m+n)(m-n) = 3\cdot 5\cdot 7$

4 Solutions :

Solve them by yourself.

$m-n = 1$, $m+n = 3\cdot 5\cdot 7$.

$m-n = 3$, $m+n = 5\cdot 7$-

$m-n = 5$, $m+n = 3\cdot 7$.

$m-n = 7$, $m+n = 3\cdot 5$.

But notice those $m^2 - n^2$, it's clear that $m$ and/or $n$ could be negative - it would not change a thing, thus $4\times 4=16$ solutions in total.