On Some two way Classifications of Integers

• Published in 1959
• Added on 2020-03-13

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

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 = {1959-12-07},
	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}
}