M3 + 27Mn + N3 = 729, m and N are positive integers, M + n is greater than Mn, then M + n = () I want to go over Chen

M3 + 27Mn + N3 = 729, m and N are positive integers, M + n is greater than Mn, then M + n = () I want to go over Chen

m+n>mn
Well organized
(m-1)(n-1)0
So it's only possible
m+n=9
On the contrary, when
m=k,n=9-k(k=1,2,...,8)
All of them satisfy the original equation, so they are the solutions