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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."

Remark on the Number of Classes of Binary Quadratic Forms of a Given Negative Determinant