Hello this is my first post here. I found a problem in algebra which i cannot solve and don't even know if there are solutions as asked. It is that one: 1. The problem statement, all variables and given/known data Find all the integer solutions (x,y) that satisfy the equation: 2. Relevant equations ×3-727× = y3 - 727y 3. The attempt at a solution x3 - y3 = 727x - 727y (x-y)(x2+xy+y2)=727(x-y) I didn't divided by (x-y) because i think i'll lose solutions. Also, x-y can be zero (i think). So i finally have: (x-y)(x2+xy+y2-727)=0 How can i continue? Can i factorize more the second bracket? Or i can solve it graphically? Also, x-y=0 doesn't mean that i have infinite solutions? If i set myself x and y Ε Z .