Is there any perfect cube that becomes a perfect square if you add 7 to it?

Write the equation as y^2 + 1 = x^3 + 8 = (x+2)(x^2 - 2x + 4)

The last factor = (x + 1)^2 + 3, so it is of the form 4k + 3.

So it has some prime factor q of that form.

Posted by xdog on 2007-08-03 19:27:45