1983 AIME Problems/Problem 8
Problem
What is the largest -digit prime factor of the integer ?
Solution
Expanding the binomial coefficient, we get . Let the required prime be ; then . If , then the factor of appears twice in the denominator. Thus, we need to appear as a factor at least three times in the numerator, so . The largest such prime is , which is our answer.
Solution 2: Clarification of Solution 1
First notice that $$ (Error compiling LaTeX. Unknown error_msg)200\choose100=\frac{200!}{100!100!}=
See Also
1983 AIME (Problems • Answer Key • Resources) | ||
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