Geodesic
On Some two way Classifications of Integers
Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 85-89

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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. 
Lambek, J.; Moser, L. On Some two way Classifications of Integers. Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 85-89. doi: 10.4153/CMB-1959-013-x
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     title = {On {Some} two way {Classifications} of {Integers}},
     journal = {Canadian mathematical bulletin},
     pages = {85--89},
     year = {1959},
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     doi = {10.4153/CMB-1959-013-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-013-x/}
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