Integer Solutions of $x^4+y^4=z^2$

Asked Sep 24 '17 at 18:17

Active Sep 24 '17 at 18:17

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Show that there do not exist any non-trivial integer solutions of $x^4+y^4=z^2$

This was asked in a number theory test, so I tried showing that there can't exist any Pythagorean Triple of the form $(x^2, y^2, z)$ and using possible congruence modulos with $3, 4, 5$ etc. but every time I get some case that remains to be disproved.
Any help or hint is appreciated.

asked Sep 24 '17 at 18:17

ab123

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Other related links may be found courtesy of Approach0. – Simply Beautiful Art Sep 24 '17 at 18:21
@SimplyBeautifulArt Thanks and sorry I didn't search thoroughly, maybe this can be closed – ab123 Sep 24 '17 at 18:22
Well, take a look, if you feel satisfied with the dupe, you can click the "Yes, this answers my question" button. If not, you may find some better information in the last link. – Simply Beautiful Art Sep 24 '17 at 18:23

Integer Solutions of $x^4+y^4=z^2$

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