1985 AIME Problems/Problem 7
Problem
Assume that , , , and are positive integers such that , , and . Determine .
Solution
It follows from the givens that is a perfect fourth power, is a perfect fifth power, is a perfect square and is a perfect cube. Thus, there exist integers and such that , , and . So . We can factor the left-hand side of this equation as a difference of two squares, . 19 is a prime number and so we must have and . Then and so , and .
Video Solution by OmegaLearn
https://youtu.be/euz1azVKUYs?t=709
~ pi_is_3.14
See also
1985 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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