
Summary: Given an arbitrary irreducible integral binary quadratic form, we show how to construct, in parametric terms, arithmetic progressions of nine terms all of which can be represented by the given binary quadratic form. For certain binary quadratic forms, we can extend the length of the arithmetic progressions to 11 terms. As an example, we construct infinitely many arithmetic progressions of length 11 which can be represented by the binary quadratic form \(x^2 + y^2\).
Quadratic forms over global rings and fields, Sums of squares and representations by other particular quadratic forms
Quadratic forms over global rings and fields, Sums of squares and representations by other particular quadratic forms
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