x7 + y7 =1
x + y = 1
Find the integer value(s) of (x-y)2.
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.