# On Some two way Classifications of Integers

- Published in 1959
- Added on

In the collections

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.

## Links

- https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-some-two-way-classifications-of-integers/C36087ADE965C59BE843D73B9FA11A87#
- https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C36087ADE965C59BE843D73B9FA11A87/S0008439559051116a.pdf/div-class-title-on-some-two-way-classifications-of-integers-div.pdf

## Other information

- key
- OnSometwowayClassificationsofIntegers
- type
- article
- date_added
- 2020-03-13
- date_published
- 1959-07-11
- identifier
- doi:10.4153/CMB-1959-013-x
- journal
- Canadian Mathematical Bulletin
- publisher
- Cambridge University Press
- volume
- 2
- issue
- 2
- issn
- 1496-4287
- doi
- 10.4153/CMB-1959-013-x
- pages
- 85-89

### BibTeX entry

@article{OnSometwowayClassificationsofIntegers, key = {OnSometwowayClassificationsofIntegers}, type = {article}, title = {On Some two way Classifications of Integers}, author = {J. Lambek and L. Moser}, abstract = {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.}, comment = {}, date_added = {2020-03-13}, date_published = {1959-07-11}, urls = {https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-some-two-way-classifications-of-integers/C36087ADE965C59BE843D73B9FA11A87{\#},https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C36087ADE965C59BE843D73B9FA11A87/S0008439559051116a.pdf/div-class-title-on-some-two-way-classifications-of-integers-div.pdf}, collections = {Fun maths facts,Integerology}, url = {https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-some-two-way-classifications-of-integers/C36087ADE965C59BE843D73B9FA11A87{\#} https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C36087ADE965C59BE843D73B9FA11A87/S0008439559051116a.pdf/div-class-title-on-some-two-way-classifications-of-integers-div.pdf}, year = 1959, urldate = {2020-03-13}, identifier = {doi:10.4153/CMB-1959-013-x}, journal = {Canadian Mathematical Bulletin}, publisher = {Cambridge University Press}, volume = 2, issue = 2, issn = {1496-4287}, doi = {10.4153/CMB-1959-013-x}, pages = {85-89} }