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Number Theory Open

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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  1. 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

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