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An arithmetic sum with an application to quasi k-free integers

Published online by Cambridge University Press:  09 April 2009

V. C. Harris  and
M. V. Subbarao
V. C. Harris
Affiliation:
San Diego State College, San Diego, California, U.S.A.
M. V. Subbarao
Affiliation:
University of Alberta, Edmonton, Alberta, Canada
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Let n be a positive integer and let T be any nonempty set of positive integers. By (n, T) = 1 we men n is relatively prime to each element of T. Hence n can be written as n = n1n2 where n1 is the largest divisor of n such that (n1, T)= 1. Let P be a property associated with positive integers. We shall say that a positive integer n is a P-number if it satisfies the property P. If in the above representation of n, the integer n1 is a P-number. then we shall say that n is a quasi P-number relative to T, or, simply, a quasi P-number. In particular, for k a positive integer >1, n is quasi k-free for given set T) if n1 is k-free.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 272 - 278
Copyright
Copyright © Australian Mathematical Society 1973

References

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