1987 AIME Problems/Problem 5
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Problem
Find if and are integers such that .
Solution
If we move the term to the left side, it is factorable with Simon's Favorite Factoring Trick:
is equal to . Since and are integers, cannot equal a multiple of three. doesn't work either, so , and . This leaves , so . Thus, .
Video Solution by OmegaLearn
https://youtu.be/ba6w1OhXqOQ?t=4699 ~ pi_is_3.14
Video Solution
https://youtu.be/z4-bFo2D3TU?list=PLZ6lgLajy7SZ4MsF6ytXTrVOheuGNnsqn&t=3704 - AMBRIGGS
See also
1987 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.