This is a result of Singmaster (American Math Monthly, 1971).

 Here is his proof ($N(a)$ is the number of times $a$ appears.) This result has since been much improved, see the [wikipedia article on Singmaster's conjecture.][1]

[![enter image description here][2]][2]


  [1]: https://www.wikiwand.com/en/Singmaster%27s_conjecture
  [2]: https://i.sstatic.net/MrceL.png