I'm revising for exams and I've got stuck on an algebraic number theory question. The equation I'm trying to solve is $$ x^2 -2 = y^3, $$ and I was told to rewrite it as $$ x^2 + 6(y+1)^2 = (y+2)^3. ...
I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...