Can you prove it?

Number Theory Level 3

How many non-zero integer solutions exists for the equation x 4 + y 4 = z 2 x^4+y^4=z^2

Bonus : How many non-zero integer solutions exists for the equation x 4 − y 4 = z 2 x^4-y^4=z^2

6 1 infinite 5 3 0 2 4

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1 solution

Aaghaz Mahajan
May 7, 2018

(x^2, y^2, z) should form a Pythagorean triplet.......but it is known that in any Pythagorean triplet, there exists at-most one perfect square.......

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