Are solutions of the Diophantine equation $x^4+y^4+z^4=2t^4$ well-known?
I give a solution:
$x=m^2-n^2, y=m^2-2mn, z=n^2-2mn, t=m^2+n^2-mn$
Asked
Active
Viewed 183 times
2
-
2MathWorld says "there are many solutions" – Carlo Beenakker Jun 24 '17 at 17:38
-
6This is an example of a K3 surface. You have found a copy of $\mathbb P^1_{\mathbb Q}$ sitting inside the surface. A general conjecture says that there is some number field $K/\mathbb Q$ such that the $K$-rational points on the surface are Zariski dense. If you are interested in questions of this sort, you should read about K3 surfaces, both their geometry and their arithmetic. – Joe Silverman Jun 24 '17 at 18:17
-
2Possible duplicate of Parametrizing the solutions to a diophantine equation of degree four – jeq Jun 25 '17 at 01:25