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ON PAIRS OF LINEAR EQUATIONS IN FOUR PRIME VARIABLES AND POWERS OF TWO

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  22 March 2012

YAFANG KONG
YAFANG KONG*
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong (email: [email protected])
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Abstract

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In this paper, we consider the simultaneous representation of pairs of positive integers. We show that every pair of large positive even integers can be represented in the form of a pair of linear equations in four prime variables and k powers of two. Here, k=63 in general and k=31 under the generalised Riemann hypothesis.

Keywords

linear equationsHardy–Littlewood methodprimespowers of two

MSC classification

Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 55 - 67
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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