Maximum size of a set of integers with no two adding up to a square
Also appears in collections : Additive combinatorics in Marseille / Combinatoire additive à Marseille, Exposés de recherche
Erdös and Sárközy asked the maximum size of a subset of the first $N$ integers with no two elements adding up to a perfect square. In this talk we prove that the tight answer is $\frac{11}{32}N$ for sufficiently large $N$. We are going to prove some stability results also. This is joint work with Simao Herdade and Ayman Khalfallah.
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