engleski

An extension of an old problem of Diophantus and Euler. II

Diophantus found three rationals 3/10, 21/5, 7/10 with the property that the product of any two of them increased by the sum of those two gives a perfect square, and Euler found four rationals 65/224, 9/224, 9/56, 5/2 with the same property. In this paper we construct an infinite family of rational quintuples with the same property. The construction is based on the fact that there are infinitely many rational points on the curve y^2 = -(x^2-x-3)(x^2+2x-12)

Eulerian quintuples; Diophantine quintuples; elliptic curves

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