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In mathematics, Kummer's theorem on binomial coeffients gives the highest power of a prime number p dividing a binomial coefficient. In particular, it asserts that given integers n ≥ m ≥ 0 and a prime number p, the maximum integer k such that p^k divides the binomial coefficient $(\genfrac{}{}{0ex}{}{n}{m})$ is equal to the number of carries when m is added to n − m in base p.

The theorem is named after Ernst Kummer, who proved it in the paper Template:Harvtxt.

See also

• Lucas's theorem on binomial coefficients

External links

• Template:PlanetMath

References

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