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11
votes
Accepted
A sumset inequality
The proposed inequality is not true. I do not claim originality for this example: all I have done is take Seva's observation that the inequality would imply an improvement $|3A|\leq K^2|A|$ given $|2A …
5
votes
Accepted
Partition regular systems: do they have solution in (very dense) set of integers?
This doesn't have anything to do with partition regularity: There is such a constant $C(A)<1$ provided only that there exists at least one solution to $Ax=0$ in positive integers.
Indeed suppose $x = …