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OP-7565Status unassessedCombinatorics

Rudin's problem for Fp[x],p>2\mathbb{F}_p[x], p>2

Additive combinatorics and its applications · Historical workshop question

MSC 05 · Combinatorics

Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/addcombapp/ Not an author-supplied MSC code.

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓
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Problem statement

Suppose A⊂Fp[x]A\subset \mathbb{F}_p[x] is of finite size, and every element of AA is a square. Show that ∣A+A∣≥∣A∣1+ϵ|A+A|\geq |A|^{1+\epsilon} for some constant ϵ\epsilon.

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Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

Status note in the source

We know that Ruzsa's modeling theorem, and 4AP4AP conjecture, implies the given problem.

References
  1. [1]Additive combinatorics and its applications link

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