Sets whose differences avoid squares modulo 𝑚
Copyright policy )Sets whose differences avoid squares modulo 𝑚
We prove that if ε ( m ) → 0 \varepsilon (m)\to 0 arbitrarily slowly, then for almost all m m and any A ⊂ Z m A\subset \mathbb {Z}_m such that A − A A-A does not contain non-zero quadratic residues we have | A | ⩽ m 1 / 2 − ε ( m ) . |A|\leqslant m^{1/2-\varepsilon (m)}.
- Steklov Mathematical Institute Russian Federation
- Department of Mathematical Sciences Russian Federation
- University of Illinois at Urbana–Champaign United States
- University of Illinois at Urbana Champaign United States
Mathematics - Number Theory, Power residues, reciprocity, FOS: Mathematics, probabilistic number theory, Mathematics - Combinatorics, Exponential sums, additive number theory, Number Theory (math.NT), Combinatorics (math.CO), Sequences (mod \(m\))
Mathematics - Number Theory, Power residues, reciprocity, FOS: Mathematics, probabilistic number theory, Mathematics - Combinatorics, Exponential sums, additive number theory, Number Theory (math.NT), Combinatorics (math.CO), Sequences (mod \(m\))
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