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On the number of square-full integers between successive squares

Published online by Cambridge University Press:  26 February 2010

P. Shiu
P. Shiu
Affiliation:
Mathematics Department, Loughborough University, Leicestershire LE11 3TU, England
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Extract

A positive integer n is called a square-full integer, if p2 divides n, whenever p is a prime divisor of n. It is clear that each square-full integer can be written in the form a2b3, where a and b are positive integers; moreover, this representation is unique if we stipulate that b is square-free.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 171 - 178
Copyright
Copyright © University College London 1980

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References

1.Bateman, P. T. and Grosswald, E.. “On a theőrem of Erdos and Skeres”, Illinois J. Math., 2 (1958), 88–89.Google Scholar
2.Cassels, J. W. S.. An introduction to Diophantine approximation. Cambridge Tracts in Mathematics no. 45. (Cambridge, 1957).Google Scholar
3.Erdős, P. and Szekeres, S.. “über die Anzahl der Abelchen Gruppen gegebener Ordnung und über ein verwandtes zahlentheorestisches Problem”, Ada Scient. Math. Szeged, 7 (1935), 95–102.Google Scholar
4.Kendall, D. G. and Rankin, R. A.. “On the number of Abelian groups of a given order”, Quart. J. of Math. (Oxford), 18 (1947), 197–208.Google Scholar
5.Ryser, H. J.. Combinational mathematics, Carus Math. Monographs (Math. Assoc. of America, 1963).CrossRefGoogle Scholar