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Bounds on size of subset of additive set that is sum-free


Jan 26, 2012
Hey, I was reading about this is in "Additive Combinatorics" (Additive Combinatorics (Cambridge Studies in Advanced Mathematics): Terence Tao, Van H. Vu: 9780521136563: Amazon.com: Books) on pg. 4 when I went to the references and found this paper (http://renyi.mta.hu/~p_erdos/1965-02.pdf) which proves the statement starting at the bottom of the 6th page. The proofs look very different, but I feel like the same ideas might be being developed. A couple questions:

In Tao's proof, I'm not sure why $x^{-1}a$ is uniformly distributed in Z_p\{0}

In Erdos's, I am unfamiliar with this notation, "a_r,alpha (mod 1)".

Any suggestions? Thx