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Number Theory
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Singmaster's Conjecture
Is there a uniform bound on how often a number greater than 1 can appear in Pascal's triangle? Singmaster asked whether the multiplicity of values in binomial coefficients is bounded.
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- Validated increment
Highest known multiplicities still small; bound unproved
Known numbers with high multiplicity in Pascal's triangle remain rare and small. Conditional and average-order results exist; a uniform absolute bound is open.
Previous best
No uniform bound; record multiplicities are single-digit
New certified
Same qualitative picture: records catalogued, bound open
Public literature baseline
Also open