Abstract
IN NATURE of July 21 (vol. 107, p. 652) appears a letter from Mr. W. E. H, Berwick, inquiring whether the values of y, z satisfying the equation z2 — py2 = —4, which are derivable from Gauss's cyclotomic formulæ, constitute generally the primitive solution of this equation. In reply I have to point out that a comparison of Gauss's formulæ (Mathews, “Theory of Numbers,” p, 215) with Kronecker's formula (Mathews, p. 253), where T2 — DU2 = 4 is the primitive solution of this equation, T and U being positive, shows that z, y are connected with the primitive solution a, b by the relation where h is the number of properly primitive classes of determinant p. Incidentally, it appears that z is always positive and y negative.
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WHITEHEAD, R. An Algebraical Identity. Nature 108, 212 (1921). https://doi.org/10.1038/108212b0
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DOI: https://doi.org/10.1038/108212b0
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