Looks like Pythagoras

Number Theory Level 4

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

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

1 solution

Jake Lai
Mar 18, 2015

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

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

Department 8 - 5 years, 11 months ago

Looks like Pythagoras

1 solution

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