gamma11
11-17-2006, 09:04 PM
Please teach me how to solve this question. Thank you very much.
Prove that if x^3 + y^3 = z^3, and x , y, z are quadratic integers in Q[sqrt(-3)]
, then alpha = (3+sqrt(-3))/2 is belonging to Q[sqrt(3)] must divide one of x, y, or z.
Hint: Reduce the equation modulo alpha^3.
Prove that if x^3 + y^3 = z^3, and x , y, z are quadratic integers in Q[sqrt(-3)]
, then alpha = (3+sqrt(-3))/2 is belonging to Q[sqrt(3)] must divide one of x, y, or z.
Hint: Reduce the equation modulo alpha^3.