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ASU 469 All Soviet Union MO 1988 x^5+y^5=2x^2y^2 =>(1-xy) rational's square

Source:

August 7, 2019

rationalsquarenumber theory

Problem Statement

If rationals

x, y

satisfy

x^5 + y^5 = 2 x^2 y^2

, show that

1-x y

is the square of a rational.