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math.NT2024
Additive Bases: Change of Domain
Boris Bukh, Peter van Hintum, Peter Keevash
We consider two questions of Ruzsa on how the minimum size of an additive basis of a given set depends on the domain of . To state these questions, for an abelian group…
math.NT2007
Sums of dilates
Boris Bukh
The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrar…
math.NT2007★ 7 cited
Non-trivial solutions to a linear equation in integers
Boris Bukh
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 dependin…