George Shakan

activity

20142022

most citedSum of dilates in vector spaces

2 citations · 4 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2022★ 2 cited

On the largest sum-free subset problem in the integers

George Shakan

Let $A \subset Z_{> 0}$ of size $n$ . It is conjectured that for any $C > 0$ and $n$ large enough that $A$ contains a sum-free subset of size at least $n /3 + C$ . We study this…

math.NT2016

A lower bound for the least prime in an arithmetic progression

Junxian Li, Kyle Pratt, George Shakan

Fix $k$ a positive integer, and let $ℓ$ be coprime to $k$ . Let $p (k, ℓ)$ denote the smallest prime equivalent to $ℓ (mod k)$ , and set $P (k)$ to be the maximum of all the $…

math.NT2014★ 2 cited

Sum of dilates in vector spaces

Antal Balog, George Shakan

Let $d \geq 2$ , $A \subset Z^{d}$ be finite and not contained in a translate of any hyperplane, and $q \in Z$ such that $∣ q ∣ > 1$ . We show $$|A+ q \cdot A| \geq (|q|…