High Quality Content by WIKIPEDIA articles! In combinatorial number theory, Singmaster's conjecture, named after David Singmaster, says there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). It is clear that the only number that appears infinitely many times in Pascal's triangle is 1, because any other number x can appear only within the first x + 1 rows of the triangle. Paul Erd?s said that Singmaster's conjecture is probably true but he suspected it would be very hard to prove.

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