most recent 30 from http://mathoverflow.net 2013-06-19T05:57:39Z http://mathoverflow.net/feeds/user/14413 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61794/the-diophantine-eq-x4-y4-1z2 fermatII 2011-04-15T08:38:45Z 2012-01-16T09:43:53Z

<p>The background of this question is this: Fermat proved that the equation, $$x^4 +y^4=z^2$$<br> has no solution in the positive integers. If we consider the near-miss, $$x^4 +y^4-1=z^2$$<br> then this has plenty (in fact, an infinity, as it can be solved by a Pell equation). But J. Cullen, by exhaustive search, found that the other near-miss, $$x^4 +y^4 +1=z^2$$<br> has none with $0 &lt; x,y &lt; 10^6$ .</p> <p>Does the third equation really have none at all, or are the solutions just enormous?</p>