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Sequence of binomial coefficients

Source: 54 Polish MO 2003 Second Round - First Day Problem 1

April 21, 2018

number theorybinomial coefficientsPoland

Problem Statement

Prove that exists integer

n > 2003

that in sequence

\binom{n}{0}

\binom{n}{1}

\binom{n}{2}

, ...,

\binom{n}{2003}

each element is a divisor of all elements which are after him.