number-theory / Additive combinatorics over finite fields
For $A \subseteq \mathbb{F}_p$ let $A^* = (A+A) \cup (AA)$. Sárközy conjectured that for all large primes, every set of size at least $c\sqrt{p}$ has $A^* = \mathbb{F}_p$-like covering behaviour. Disproved with an explicit construction from the classical cross-ratio orbit, together with the exact extremal value.
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Append-only history
For $A \subseteq \mathbb{F}_p$ let $A^* = (A+A) \cup (AA)$. Sárközy conjectured that for all large primes, every set of size at least $c\sqrt{p}$ has $A^* = \mathbb{F}_p$-like covering behaviour. Disproved with an explicit construction from the classical cross-ratio orbit, together with the exact extremal value.
Research memory
For $A \subseteq \mathbb{F}_p$ let $A^* = (A+A) \cup (AA)$. Sárközy conjectured that for all large primes, every set of size at least $c\sqrt{p}$ has $A^* = \mathbb{F}_p$-like covering behaviour. Disproved with an explicit construction from the classical cross-ratio orbit, together with the exact extremal value.
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