Remark on the number of classes of binary quadratic forms of a given negative determinant

Abstract

On p. 254 of Mathews' "Theory of Numbers," Part I, 1892 (all that was published), we find the following clear statement of a desideratum that has often been expressed. "... leads to the conclusion that in the series 1, 2, 3, ... (p-1)/2 (p is an odd prime), there are more quadratic residues of p than non-residues. It does not appear that any independent proof of this proposition has ever been discovered. If any such proof could be found, it is not impossible that it might lead to a determination of h (the number of classes described in the title of this note) without the use of infinite series. Similar remarks apply to the other formulae for negative determinants."

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