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Number Theory Level 3

Find the sum of all positive integral solutions of the equation x 4 − 4 y 4 = z 2 x^4-4y^4=z^2


The answer is 0.

Marc Vince Casimiro by Marc Vince Casimiro , 22, Philippines

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2 solutions

Fox To-ong
Jan 14, 2015

according to Fermat's last theorem, there are no possible positive solutions in the equation

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Beringer Krebs
Jan 8, 2015

Well no matter which positive numbers you put in for the solution, since all the powers are even, you're also going to have a negative number which will give you the same solution. And adding a positive number to its negative is always going to give you zero. Therefore the sum of all the numbers is always going to be zero.

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Essentially incorrect. The question asks for positive integral solutions.

Utkarsh Gupta - 6 years, 5 months ago

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