- #1

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## Homework Statement

Given:

x

^{7}+ y

^{7}=1

x + y = 1

Find the integer value(s) of (x-y)

^{2}.

## Homework Equations

## The Attempt at a Solution

I thought of substituting for y and then finding the rational roots but then I realized x and y don't have to be rational numbers for (x-y)^2 to be an integer. I am 90% sure the only solution is 1 (when x=1,y=0 or x=0,y=1) but don't know how to prove it. Any hint? Thanks.