Non-trivial solutions to a linear equation in integers

Details Non-trivial solutions to a linear equation in integers Non-trivial solutions to a linear equation in integers

2007-03-26

arxiv.org/abs/math/0703767v2

Mathematics

Number Theory

5 pages, typos corrected, stronger result given

Scientific paper

For k>=3 let A \subset [1,N] be a set not containing a solution to a_1
x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that
there is an epsilon>0 depending on the coefficients of the equation such that
every such A has O(N^{1/2-epsilon}) elements. This answers a question of I.
Ruzsa.

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