Integers Uniquely Represented by Certain Ternary Forms

Kaplansky, Irving

doi:10.1007/978-3-642-60408-9_6

Integers Uniquely Represented by Certain Ternary Forms

Irving Kaplansky³

Chapter

938 Accesses

Part of the book series: Algorithms and Combinatorics ((AC,volume 13))

Abstract

This paper has no connection with the two papers jointly authored by Paul Erdös and myself; nor does it overlap any of the many conversations we had. But I feel it is appropriate to dedicate the paper to him. It has the flavor of the mathematics we both particularly enjoyed: very explicit problems challenging us to answer “yes” or “no”.

This is a preview of subscription content, log in via an institution.

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 74.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Steven Arno, The imaginary quadratic fields of class number 4, Acta Arithmetica 60 (1992), 321–334.
MathSciNet MATH Google Scholar
Paul T. Bateman and Emil Grosswald, Positive integers expressible as a sum of three squares in essentially one way, J. of Number Theory 19 (1984), 301–308.
Article MathSciNet MATH Google Scholar
E. T. Bell, The numbers of representations of integers in certain forms ax ² + by ² + cz ² Amer. Math. Monthly 31 (1924), 126–131.
Article MathSciNet MATH Google Scholar
Leonard Eugene Dickson, Modern Elementary Theory of Numbers, Univ. of Chicago Press, 1939.
Google Scholar
Burton W. Jones, The number of representations by certain positive ternary quadratic forms, Amer. Math. Monthly 36 (1929), 73–77.
Article MathSciNet MATH Google Scholar
Burton W. Jones, The Arithmetic Theory of Quadratic Forms, Carus Monograph 10, Math. Assoc. of America, 1950.
Google Scholar
G. A. Lomadze. Formulas for the number of representations of numbers by certain regular and semi-regular ternary quadratic forms belonging to two-class genera, Acta Arith. 34 (1977), 131–162. (Russian).
MathSciNet Google Scholar
Gordon Pall, Representation by quadratic forms, Can. J. of Math. 1 (1949), 344–364.
Article MathSciNet MATH Google Scholar
J. V. Uspensky, On the number of representations of integers by certain ternary quadratic forms, Amer. J. of Math 51 (1929), 51–60.
Article MathSciNet MATH Google Scholar
R. F. Whitehead, On the number of solutions in positive integers of the equation yz + zx + xy = n, Proc. Lon. Math. Soc 21 (1922), xx.
Google Scholar

Download references

Author information

Authors and Affiliations

Mathematical Sciences Research Institute, 94720, Berkeley, California, USA
Irving Kaplansky

Authors

Irving Kaplansky
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

AT&T Bell Laboratories, 600 Mountain Avenue, NJ 07974, Murray Hill, USA
Ronald L. Graham
Department of Applied Mathematics, Charles University, Malostranske nam. 25, 11800, Praha, Czech Republic
Jaroslav Nešetřil

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Kaplansky, I. (1997). Integers Uniquely Represented by Certain Ternary Forms. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös I. Algorithms and Combinatorics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60408-9_6

Download citation

DOI: https://doi.org/10.1007/978-3-642-60408-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64394-1
Online ISBN: 978-3-642-60408-9
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics