Question

How many ordered sets of integers (x,y) are there such that there exists a (positive) prime number p satisfying x(x+y)=2(y2+15p)?

Answer 1

well\[x(x+y)-2y^2=30p\]\[x^2-y^2+xy-y^2=30p\]\[(x-y)(x+y)+y(x-y)=30p\]\[(x-y)(x+2y)=30p\]