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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The forms $x+32y^2$ and $x+64y^2$


Author: Irving Kaplansky
Journal: Proc. Amer. Math. Soc. 131 (2003), 2299-2300
MSC (2000): Primary 11E16
Published electronically: February 5, 2003
MathSciNet review: 1963780
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  • 1. A. Aigner, Zahlentheorie, de Gruyter, 1975. MR 56:2901
  • 2. P. Barrucand and H. Cohn, Note on primes of type $x^2+32y^2$, class number and residuacity, J. Reine Angew. Math. 238 (1969), 67-70. MR 40:2641
  • 3. G. Lejeune Dirichlet, Über den biquadratischen Character der Zahl ``Zwei'', in Werke vol. II, Chelsea reprint, 1969, pp. 257-258. MR 40:2514
  • 4. R. J. Evans, The $2^r$-th character of $2$, J. Reine Angew. Math. 315 (1980), 174-189. MR 81f:10006
  • 5. C. F. Gauss, Theorie der biquadratischen Reste, I, in Arithmetische Untersuchungen, Chelsea reprint, 1969, pp. 511-533. (This translation by H. Maser of the Disquisitiones also contains several of Gauss' papers.)
  • 6. H. Hasse, Der $2^n$-te Potenzcharacter der $2^n$-ten Einheitswurzeln, Rend. Circ. Mat. Palermo 7 (1958), 185-244. MR 21:4143
  • 7. A. L. Whiteman, The sixteenth power residue character of $2$, Canad. J. Math. 6 (1954), 364-373. MR 16:14a

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Additional Information

Irving Kaplansky
Affiliation: Mathematical Sciences Research Institute, Berkeley, California 94720
Email: kap@msri.org

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07022-9
PII: S 0002-9939(03)07022-9
Received by editor(s): April 30, 2002
Received by editor(s) in revised form: August 15, 2002
Published electronically: February 5, 2003
Communicated by: Lance W. Small
Article copyright: © Copyright 2003 American Mathematical Society