<s>[INST] Find all solutions to $m^2 − n^2 = 105$, for which both m and n are integers Can I get a little help for  this question? 
Find all the integer solutions to $m^2 − n^2 = 105$.
 [/INST] $(m+n)(m-n) = 105$
$(m+n)(m-n) = 3\cdot 5\cdot 7$
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. 
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