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ON WARING’S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

Part of: Additive number theory; partitions Multiplicative number theory

Published online by Cambridge University Press:  28 June 2013

John B. Friedlander  and
Trevor D. Wooley
John B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto ON,Canada, M5S 2E4 email frdlndr@math.toronto.edu
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW,U.K. email matdw@bristol.ac.uk
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Abstract

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott–Halberstam conjecture, we show that all large natural numbers $n$ with $8\nmid n$, $n\not\equiv 2~(\text{mod} ~3)$ and $n\not\equiv 14~(\text{mod} ~16)$ are the sum of two squares and three biquadrates.

MSC classification

Secondary: 11P05: Waring's problem and variants 11N36: Applications of sieve methods 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014 , pp. 153 - 165
Copyright
Copyright © University College London 2013 

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