Four rational squares in arithmetic progressions and a\xa0family of elliptic curves with positive Mordell-Weil rank

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We study the question at which relative distances four squares of rational numbers can occur as terms in an arithmetic progression. This number-theoretical problem is seen to be equivalent to finding rational points on certain elliptic curves. Both number-theoretical results and results concerning the associated elliptic curves are derived; i.e., the correspondence between rational squares in arithmetic progressions and elliptic curves is exploited both ways.