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diophantine x^2 = y 2^z + 1

Source: 41st Austrian Mathematical Olympiad National Competition (Final Round, part 2) 2nd June 2010 p2

September 5, 2019
number theoryDiophantine equationdiophantine

Problem Statement

Determine all triples (x,y,z)(x, y, z) of positive integers x>y>z>0x > y > z > 0, such that x2=yā‹…2z+1x^2 = y \cdot 2^z + 1
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