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The Diophantine quintuple conjecture Diophantus of Alexandria, who was a 3rd century Greek mathematician. Diophantus himself noticed that the quadruple of rational numbers {1/16, 33/16, 17/4, 105/16} has the property that the product of any two of them plus one is the square of a rational number, and since then, collections of six positive rational numbers with the same property have been found. The set of integers {1,3,8,120} has the property that the product of any two of them is one less than
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