I believe this is a problem from an International Mathematical Olympiad. [Don't know the year].
$p \ge 5$ is a prime number.
Show that
$$ \sum_{k=1}^{\lfloor 2p/3 \rfloor} \binom{p}{k}$$ is divisible by $p^2$.
[Solution]
$p \ge 5$ is a prime number.
Show that
$$ \sum_{k=1}^{\lfloor 2p/3 \rfloor} \binom{p}{k}$$ is divisible by $p^2$.
[Solution]
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