What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.12
Let $G$ be an abelian group of size $N$, and suppose that $A \subset G$ has density $\alpha$. Are there at least $\alpha^{15} N^{10}$ tuples $(x_1, ..., x_5, y_1, ..., y_5) \in G^{10}$ such that $x_i + y_j \in A$ whenever $j \in \{i, i + 1, i + 2\}$?
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What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.12
Let$G$ be an abelian group of size $N$ , and suppose that $A \subset G$ has density $\alpha$ . Are there at least $\alpha^{15} N^{10}$ tuples $(x_1, ..., x_5, y_1, ..., y_5) \in G^{10}$ such that $x_i + y_j \in A$ whenever $j \in \{i, i + 1, i + 2\}$ ?
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Choose either option