On square values of quadratics

Abstract

Let N be a positive integer. We enquire whether there is a quadratic f(t)=at2 + bt + c, not identically square, which takes square values for N consecutive integers t. In [1] it was shown that this was possible, in what we shall call the symmetric case, if N = 8. A better treatment of this case appears here, together with a discussion of the nonsymmetric case, where we may take N = 7. There is no evidence that these are the best possible results.