Star of David theorem

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 Henry W. Gould in 1972.

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+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

References

External links