parmenides51 24.08.2019 15:14 Determine all pairs $(m, n)$ of positive integers for which $(m + n)^3 / 2n (3m^2 + n^2) + 8$
Math-wiz 24.08.2019 15:23 Assuming / stands for divides, The only solutions are $(m,n)=(1,1),(n+2,n)\forall n$
Math-wiz 24.08.2019 17:59 hint Write $\frac{2n(3m^2+n^2)+8}{(m+n)^3}=k$ Multiply, keep only 8 on RHS. Try proving that if $k\geq 2$, then $m,n<2$, i.e., $(m,n)=(1,1)$, and the case $k=1$ is easy