On a theorem of Birch concerning sums of distinct integers taken from certain sequences
Published online by Cambridge University Press: 28 June 2011
Extract
In [1] B. J. Birch, solving in the affirmative a conjecture of Erdὅs, proved the following result:
Theorem 1. Let p and q be coprime integers greater than 1. Then every large natural number may be written as a sum of distinct terms of type paqb.
In fact Birch pointed out that, with similar arguments, one could obtain a stronger version where the exponent b of q can be bounded in terms of p and q. The proofs were entirely elementary.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 199 - 206
- Copyright
- Copyright © Cambridge Philosophical Society 1989
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