![](/files/happy5.png)
Pascal's triangle
Singmaster's conjecture ★★
Author(s): Singmaster
Conjecture There is a finite upper bound on the multiplicities of entries in Pascal's triangle, other than the number
.
![$ 1 $](/files/tex/f81bea742c6e484717a25f7b16835462361c1d2e.png)
The number appears once in Pascal's triangle,
appears twice,
appears three times, and
appears
times. There are infinite families of numbers known to appear
times. The only number known to appear
times is
. It is not known whether any number appears more than
times. The conjectured upper bound could be
; Singmaster thought it might be
or
. See Singmaster's conjecture.
Keywords: Pascal's triangle
![Syndicate content Syndicate content](/misc/feed.png)