Star of David theorem
The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by H.W. Gould in 1972.
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Statement
The greatest common divisors of binomial coefficients forming the Star of David shape in Pascal's triangle, are equal:
![\begin{align}
& {} \quad \gcd\left\{ \binom{n-1}{k-1}, \binom{n}{k%2B1}, \binom{n%2B1}{k}\right\} \\[8pt]
& = \gcd\left\{ \binom{n-1}{k}, \binom{n}{k-1}, \binom{n%2B1}{k%2B1}\right\}.
\end{align}](/2012-wikipedia_en_all_nopic_01_2012/I/01d7b3bc539e33888f5804160b66af50.png)
See also
References
- H.W. Gould, A New Greatest Common Divisor Property of The Binomial Coefficients, Fibonacci Quarterly 10 (1972), 579–584.
- Star of David theorem, from MathForum.
- Star of David theorem, blog post.