1983 AIME Problems/Problem 8
Problem
What is the largest 2-digit prime factor of the integer ?
Solution
Expanding the binomial coefficient, we get . Let the prime be
; then
. If
, then the factor of
appears twice in the denominator. Thus, we need
to appear as a factor three times in the numerator, or
. The largest such prime is
, which is our answer.
See also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |