By Ladoshkin M.V.

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Evans, A. Martin, G. Hart, S. BiUs, Educ. Times 16 (1872), p. 34; 23 (1875), p. 98,109; 28 (1877), p. 29; C. Moreau, Nouv. ann. 330; C. Minnigerode, Gott. Nachr. 1873, p. 619; W. Schnnidt, Zeitschr. Math. Phys. 92; H. J. S. Smith, Lond. Math. Soc. Proc. 7 (1876), p. 199 = ColI. Math. Pap. 2, p. 148; S. Roberts 15 (1884), p. 247; H. B"ocard, Nouv. Corr. Math. 4 '(1878), p. 161, 193, 228, 337; S. BeaUs 6 (1880), p. 306, 342; W. Dwrfee, John Hopk. Circ. 18821, p. 178; A. Meyer, ZUrich Naturf. Ges.

Math. u. naturw. ADz. 14 (1896), p. 26; Ungar. Ber. 14 (1898 [1895/96]), p. -Kongr. Verh. 1898 [1897], p. 163. 20) Gauss, Disqu. arithm. art. 226 = Werke 1, p. 226. 21) A. Cayley, J. f. Math. 32 (1846), p. 122 = Pap. 1, p. 382; 50 (1855), p. 288, 299, bes. p. 311 = Pap. 2, p. 192, 202; H. Taber, Chic. Congr. Pap. (1896 [1893]), p. 395 [1 B 2, Nr .. 41-46]. 3S" I C 2. Arithmetische Theorie der Formen. 596 Die Fundamentalgleichung einer solchen Substitution ist reziprok 22 ). , n) k m sich transformiert (Rosanes) 22).

2, 7] der Form t u deren Norm t2 - Du 2 absolut gleich Eins ist, ist die Frage nach den "Einheiten" des "Bereiches" VIJ . Da auch Zahlen + YD, von der Form man fUr D t + ~ -yD "ganze" algebraische Zahlen sein konnen, hat 0 oder 1 (mod. -Du! = 1 + 4 - zu betrachten 32). Man beschrankt sich auf die "eigentlichen" Auflosungen, in denen u ungerade ist. 1st (T", U") die kleinste Auflosung dieser Gleichungen, und ist T"2-DU"2 4 so erhalt man aus =+ 1, (T"+ ~"lCQr fiir k = 1, 2, 4, 5, 7, 8, . . alle eigentlichen positiven Auflosungen l ' h ung tt-Du 3 6 ,v,...

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A-modules over A-algebras and Hochschild cohomology for modules over algebras by Ladoshkin M.V.


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