Difference between revisions of "2015 AIME I Problems/Problem 3"
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Revision as of 12:38, 20 March 2015
Problem
There is a prime number such that is the cube of a positive integer. Find .
Solution
We call the positive integer mentioned . Then .
Factoring the left side:
We can then try setting one of the factors to , starting with .
We get
Then our other factor is . A quick divisibility search shows that is prime, so our answer is