Prove that for every integer x, there is an integer y such that (y^2-2)/(x^4+1) is an integer.

For the first integer solution greater than zero for the expression (y² - 2)/(x⁴ + 1), I noticed it equivalent to (y - x)/x. 

By observation of the latter expression, (but for where x = 0) it can be seen that there must be an integer solution y for every x.  As it is, there are multiple solutions for many values of x (to include where x=0).  Yet, how to prove the case I will leave up to the site-member or visiting math gurus.

Posted by Dej Mar on 2007-05-20 17:33:00