The question read "show that $19m^2+95mn+2000n^2=1995$ has no integer solution for $n$ and $m$." I have attempted a solution and would like to check if it is correct.
$95mn +2000n^2 = 1995-19m^2$ now factorize both sides $5n(19m+400n) = 19(105-m^2)$ From here I tried all parity cases for $m$ and $n$ and constantly end up with $odd = even$ or $even = odd$.
Is this correct? Thanks.