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A NOTE ON A RESULT OF RUZSA
Published online by Cambridge University Press: 01 February 2008
Abstract
Let σA(n)=∣{(a,a′)∈A2:a+a′=n}∣, where and A is a subset of
. Erdös and Turán conjectured that, for any basis A of
, σA(n) is unbounded. In 1990, Ruzsa constructed a basis
for which σA(n) is bounded in the square mean. In this paper, based on Ruzsa’s method, we show that there exists a basis A of
satisfying
for large enough N.
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- Research Article
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- Copyright © Australian Mathematical Society 2008
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