# 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:

{\displaystyle {\begin{aligned}&{}\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{aligned}}}