Timeline for Generalizing Euclid's proof of the infinity of primes

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Dec 27, 2011 at 13:25	comment	added	user6976		I have posted a separate question mathoverflow.net/questions/84374/… .
Dec 27, 2011 at 3:06	comment	added	user6976		Actually we need to show that $A\cdot A$ contains $-1$. So the question is how large $A\cdot A$ is. I think there were results like that for cyclic groups (and recently even for nilpotent groups).
Dec 27, 2011 at 2:54	comment	added	user6976		That is a question for Green and Tao:) The density of $A$ is small, unfortunately, and so is the density of $B$. But I am not a specialist. I still think that my question has a chance to be less of a monster than, say, Goldbach's conjecture because it is about products, not sums. But I may be too naive.
Dec 27, 2011 at 2:23	comment	added	Gjergji Zaimi		I wonder if this is known, it is related to your strong conjecture, let $q$ be a large prime, let $A$ be the set of primes less than $q$ as a subset of $\mathbb Z/q\mathbb Z$ and let $B$ be the set of their inverses. is the sumset $A+B$ large? Can we prove that it is of size $O(q)$?
Dec 27, 2011 at 2:04	history	edited	user6976	CC BY-SA 3.0	added 71 characters in body; edited body
Dec 27, 2011 at 1:25	history	edited	user6976	CC BY-SA 3.0	added 2 characters in body; edited body
Dec 27, 2011 at 1:19	history	edited	user6976	CC BY-SA 3.0	added 308 characters in body
Dec 26, 2011 at 23:27	history	answered	user6976	CC BY-SA 3.0