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We discover suprising connections between three seemingly different problems:finding right triangles with rational sides in a non-Euclidean geometry,finding three integers such that the difference of the squares of any two is asquare, and the problem of finding rational points on an algebraic surface inalgebraic geometry. We will also reinterpret Euler's work on the second problemwith a modern point of view.

Non-Euclidean pythagorean triples, a problem of euler, and rational points on K3 surfaces