Dear all

I would like to know a counter example to the following integer equation where I think there is no one at all, hoping to be mistaken

PUZZLE

IF (n, m, k) are three positive distinct coprime integers ,where (m, k) are odd integers,

then the following integer equation doesn't have any solution in the whole number system as defind above

n^3 = m^3 + k^3 + 2*n*m*k

Thanking you a lot

Bassam King Karzeddin

Al-Hussein Bin Talal University

JORDAN