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On sums of two squarefull numbers

Published online by Cambridge University Press:  24 October 2008

R. C. Baker  and
J. Brüdern
R. C. Baker
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602, U.S.A.
J. Brüdern
Affiliation:
Mathematisches Institut, Bunsenstrasse 3–5, D-W-3400 Göttingen, Germany
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Extract

A natural number n is said to be squarefull if p|n implies p2|n for primes p. The set of all squarefull numbers is not much more dense in the natural numbers than the set of perfect squares but their additive properties may be rather different. We are more precise only in the case of sums of two such integers as this is the problem with which we are concerned here. Let U(x) be the number of integers not exceeding x and representable as the sum of two integer squares. Then, according to a theorem of Landau [4],

as x tends to infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 1 - 5
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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