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## 19S. Binomial Sum Divisible by Primes

E16 Prove that for any prime $p$ in the interval $\left]n, \frac {4n}{3}\right]$, $p$ divides

$\sum^{n}_{j = 0}{{n}\choose{j}}^{4}.$

Here is the official solution file (written by Darij Grinberg, Germany): pen19.pdf.