Question

What are integer solutions to this equation: x^4 - y^4 = 671?(Verify my solution, please)

Answer 1

@Zyberg is that all?

Answer 2

x^4 - y^4 = (x^2 - y^2)(x^2 + y^2);
671 = 11 * 61 (prime factors)
since x^2 - y^2 < x^2 + y^2
x^2 - y^2 = 11
(x - y)(x + y)= 11
x - y = 1, since 11 is prime and, if x + y = 1, x or y would be <= 0.
From that, x = y + 1;
2y + 1 = 11; y = 5, x = 6
Since a^2b works same as modulus, we get that answer pairs (6, 5) and (-6, -5)

Is it right or are there more answers to this?

Answer 3

@HollowDensity yes, it is everything that the problem states.

Answer 4

Yeah, looks rock solid to me.