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Is there a polynomial of degree at least and a set such that for any there is exactly one and such that ?
Source: erdosproblems.com/477
An accepted solution exists. The statement is true.
The site labels the problem SOLVED on its problem page as accessed
2026-09-09, the page last edited 5 September 2026 (OPEN in the site's export of
2026-09-04). Its commentary credits GPT, prompted independently by Price and by
pipeline-math, with proving that such an exists for and every
even ; that is the range in which Price's construction tiles the full
image, while the pipeline-math manuscript treats only. The claim
pages
pipeline-math
and Price record
the results and their acceptance;
Sekanina's
records the refereed negative answer for , and a fourth claim is
pending. The derived claim value is proved where the site's SOLVED reads as
answered, because the question asks whether such an and exist and the
accepted claims prove that they do.