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If l_{i}^2 are all rational then so is l_{10}^2

Source: Japanese MO Finals 1994

February 11, 2011
number theory proposednumber theory

Problem Statement

Five points, no three collinear, are given on the plane. Let l1,l2,…,l10l_1,l_2,\ldots ,l_{10} be the lengths of the ten segments joining any two of the given points. Prove that if l12,…,l92l_1^2,\ldots ,l_9^2 are rational numbers, then l102l_{10}^2 is also a rational number.
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