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Two Theorems on Mosaics

Published online by Cambridge University Press:  20 November 2018

B. Gordon  and
M. M. Robertson
B. Gordon
Affiliation:
University of California, Los Angeles
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The concept of a mosaic was recently introduced by A. A. Mullin (1). By the fundamental theorem of arithmetic, every integer n > 1 can be uniquely expressed in the form

where the pi are primes satisfying p1 < p2 < . . . < pr. We then express any exponents aj which are greater than unity in the same manner, and continue in this way until the process terminates. The resulting planar configuration of primes is called the mosaic of n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 1010 - 1014
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Mullin, A. A., Some related number-theoretic functions, Bull. Amer. Math. Soc., 69 (1963), 446–447.Google Scholar
2. Rosser, J. B., The rith prime is greater than n log n, Proc. London Math. Soc, 45 (1939), 21–44.Google Scholar