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It may first be stated that this article is concerned only with the irregular negative determinants which occur in the study of quadratic forms. (The technical terms used below, e.g., "determinant," "irregular," "exponent," "duplicating," "opposite," and "genera II, IV, VIII, etc.," are fully explained in Mathews, "Theory of Numbers" (Part I., 1892) on pages 59, 178, 182, 149, 68, and 132 respectively [1].) Only three examples of the above determinants have as yet been given in mathematical literature, viz., —D = 3299 (Scholz and Taussky) [2], 6075 (Pepin) [3], and 11907 (Gauss) [4]. The writer, in his Thesis for the London Ph.D. degree written in 1953, gives 55 more examples, the complete table of 58 determinants up to the limit 150,000 being: -D = 3299 6075 11907 17739 23571 2430

On irregular negative determinants of exponent 9𝑛