Lucas’s theorem

Let m,n-{0} be two natural numbersMathworldPlanetmath . If p is a prime numberMathworldPlanetmath and :


are the base-p expansions of m and n , then the following congruenceMathworldPlanetmathPlanetmathPlanetmathPlanetmath is true :


Note : the binomial coefficientMathworldPlanetmath is defined in the usual way , namely :


if xy and 0 otherwise (of course , x and y are natural numbers).

Title Lucas’s theorem
Canonical name LucassTheorem
Date of creation 2013-03-22 13:17:31
Last modified on 2013-03-22 13:17:31
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Theorem
Classification msc 11B65