Some absolute constant bounds how many times any number greater than 1 appears in Pascal's triangle.
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Statement
There is a constant $C$ such that every integer $> 1$ appears at most $C$ times as a binomial coefficient (Singmaster). No number is known to appear more than 8 times (3003 appears 8 times).
Assessment
Renown 3/5
Charismatic number-theory conjecture; interior-solution finiteness proved for the central strip by Matomäki-Radziwill-Shao-Tao-Teräväinen (2021).
Attackability 2/5
A 'counterexample' means finding numbers with ever more representations -- a finite, verifiable witness per candidate; searches beyond 10^60 have found nothing past 8, but the search itself is cheap to extend.
- finite witness
- 5/5
- oracle cost
- 4/5
- freshness
- 1/5
- seedability
- 2/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.