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On Some two way Classifications of Integers

Published online by Cambridge University Press:  20 November 2018

J. Lambek  and
L. Moser
J. Lambek
Affiliation:
McGill UniversityUniversity of Alberta
L. Moser
Affiliation:
McGill UniversityUniversity of Alberta
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In this note we use the method of generating functions to show that there is a unique way of splitting the non-negative integers into two classes in such a way that the sums of pairs of distinct integers will be the same (with same multiplicities) for both classes. We prove a similar theorem for products of positive integers and consider some related problems.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 2 , 01 May 1959 , pp. 85 - 89
Copyright
Copyright © Canadian Mathematical Society 1959

Footnotes

*

These results were obtained at the Kingston Summer Research Institute of the Canadian Mathematical Congress.

References

Note

* On the determination of numbers by their sums of a fixed order, Pacific J. of Math. 8 (1958), pp. 845-856.