Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

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

Author(s): Irving Kaplansky
Journal: Proc. Amer. Math. Soc. 131 (2003), 2299-2300.
MSC (2000): Primary 11E16
Posted: February 5, 2003
Retrieve article in: PDF

References | Similar articles | Additional information

References:

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

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11E16

Retrieve articles in all Journals with MSC (2000): 11E16

Additional Information:

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

DOI: 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
Posted: February 5, 2003
Communicated by: Lance W. Small
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google