perplexus.info :: Just Math : Fifth Powers

Fifth Powers (Posted on 2023-03-21)

Find all solutions of:
x^5+y^5=(x+y)^5
Assume x>y.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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computer exploration | Comment 1 of 3

When either x or y is zero or y = -x, the equation is true.

Other than these, the program

clc
for y=sym(-200):200
for x=y+1:200
if x^5+y^5==(x+y)^5 && x*y~=0 && x~=-y
disp([x y])
end
end
end

finds no other instances.

Of course this is not an exhaustive search.

Posted by Charlie on 2023-03-21 09:48:42

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