Saturday, 14 October 2017

number theory - Given integers x,,y s.t. x216=y3, show that x+4 and x4 are perfect cubes

Suppose x and y are some integers satisfying x216=y3. I'm trying to show that x+4 and x4 are both perfect cubes.



I know that the greatest common divisor of x+4 and x4 must divide 8, but I don't know where to go from there. Would anyone be able to help?

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