Rudin's conjecture, in additive combinatorics and elementary number theory, concerns an upper bound for the number of squares in finite arithmetic progressions. It was first stated by Walter Rudin in his 1960 paper Trigonometric Series with Gaps, and has applications in the theory of trigonometric series. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Proposed Year Progress Toward ResolutionGonzalez-Jimenez and Xarles verified the strong form in 2014 for 6 <= N <= 52; the conjecture itself remains open. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Rudin's Conjecture (Wikipedia)
Sources
1. Rudin's Conjecture (Wikipedia)
Wikimedia FoundationLead section
first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps
Background and partial results
Enrique Gonzalez-Jimenez and Xavier Xarles verified in 2014 that the Strong Rudin's Conjecture holds for all
In Branch: Number Theory, Lead sentence
njecture in additive combinatorics and elementary number theory about an upper bound for the number of squares in finite arithmeti
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