(nr) is an integer

Theorem 1.

For nr0, the binomial coefficientMathworldPlanetmath


is an integer.


The proof is by inductionMathworldPlanetmath on n. For n=0, the claim is clear. Thus, suppose the claim holds for n1. For r=1,,n, Pascal’s rule gives


That is, (n+11),,(n+1n) are integers. Since


the proof is completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath. ∎

Title (nr) is an integer
Canonical name nchooseRIsAnInteger
Date of creation 2013-03-22 15:02:01
Last modified on 2013-03-22 15:02:01
Owner matte (1858)
Last modified by matte (1858)
Numerical id 6
Author matte (1858)
Entry type Theorem
Classification msc 11B65
Classification msc 05A10