Proceedings of the American Mathematical Society

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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. Alexander Aigner, Zahlentheorie, Walter de Gruyter, Berlin-New York, 1975 (German). de Gruyter Lehrbuch. MR 0444551
  • 2. Pierre Barrucand and Harvey Cohn, Note on primes of type 𝑥²+32𝑦², class number, and residuacity, J. Reine Angew. Math. 238 (1969), 67–70. MR 0249396
  • 3. G. Lejeune Dirichlet, Mathematische Werke. Bände I, II, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften von L. Kronecker, Chelsea Publishing Co., Bronx, N.Y., 1969 (German). MR 0249268
  • 4. Ronald J. Evans, The 2^{𝑟}th power character of 2, J. Reine Angew. Math. 315 (1980), 174–189. MR 564532, 10.1515/crll.1980.315.174
  • 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. Helmut Hasse, Der 2ⁿ-te Potenzcharakter von 2 im Körper der 2ⁿ-ten Einheitswurzeln, Rend. Circ. Mat. Palermo (2) 7 (1958), 185–244 (German). MR 0105401
  • 7. A. L. Whiteman, The sixteenth power residue character of 2, Canadian J. Math. 6 (1954), 364–373. MR 0062761

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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
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