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$120, 210 ,3003$ appear $6$ times in Pascal's triangle.

$120={10\choose3}={16\choose2}={120\choose1}\\$

$210={10\choose4}={21\choose2}={210\choose1}\\$

$3003={14\choose6}={78\choose2}={3003\choose1}$

Are there any numbers $>1$ that appear more than $6$ times, and are there finitely many appearing $6$ times?

  • 5
    See [here](http://en.wikipedia.org/wiki/Multiplicities_of_entries_in_Pascal%27s_triangle). 3003 appears eight times, infinitely many numbers appears six times and it is not known whether any number appears more than eight times.2012-04-13
  • 0
    fascinating ...2012-04-13

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