Star of David theorem

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The Star of David theorem (the rows of the Pascal triangle are shown as columns here).

The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by H.W. Gould in 1972.

Statement[edit]

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+1}, \binom{n+1}{k}\right\} \\[8pt]
& = \gcd\left\{ \binom{n-1}{k}, \binom{n}{k-1}, \binom{n+1}{k+1}\right\}. 
\end{align}

See also[edit]

References[edit]

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