Question 44
For every integer $k \geq 2$, prove that $2^{3k}$ divides the number
$$
\binom{2^{k+1}}{2^{k}} - \binom{2^{k}}{2^{k-1}}
$$
$$
\binom{2^{k+1}}{2^{k}} - \binom{2^{k}}{2^{k-1}}
$$
MathNet 2007-part-02 — 187 problems (EN–VI) Question 44
Math Olympiad Vault · MathNet 2007-part-02 — 187 problems (EN–VI)