Looks like Pythagoras

For some whole numbers n n there exists whole numbers x , y , z x, y, z such that x n + y n = z n x^{n}+y^{n}=z^{n} . Which of the following is true about the possible values of n n ?

n=2 only n=2, 1, -1 n=2 and one other value There are infinitely many such n. n=1 only

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1 solution

Jake Lai
Mar 18, 2015

W = { 0 , 1 , 2 , } \mathbb{W} = \lbrace 0,1,2,\ldots \rbrace so x = y = z = 0 x = y = z = 0 satisfies the Diophantine for all n 0 n \neq 0 .

Nice, I thought the n should satisfy the Pythagoras theorem.

Department 8 - 5 years, 11 months ago

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