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1983 AIME Problems/Problem 8

Revision as of 23:06, 23 July 2006 by Joml88 (talk | contribs)

Problem

What is the largest 2-digit prime factor of the integer ${200\choose 100}$?

Solution

Expanding the binomial coefficient, we get ${200 \choose 100}=\frac{200!}{100!100!}$.

Therefore, our two digit prime $p$ must satisfy $3p<200$. The largest such prime is $61$, which is our answer.

See also

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