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(\sqrt5 +1)^{2x}+ (\sqrt5 -1)^{2x}=2^x(y^2+2) , infinite natural solutions

Source: Tuymaada 1995 p3

April 27, 2019
Diophantine equationalgebranumber theory

Problem Statement

Prove that the equation (5+1)2x+(5−1)2x=2x(y2+2)(\sqrt5 +1)^{2x}+ (\sqrt5 -1)^{2x}=2^x(y^2+2) has an infinite number of solutions in natural numbers.
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