Mock AIME 2 2006-2007 Problems/Problem 4
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Problem
Revised statement
Let and be positive real numbers and a positive integer such that , where is as small as possible and . Compute .
Original statement
Let be the smallest positive integer for which there exist positive real numbers and such that . Compute .
Solution
Two complex numbers are equal if and only if their real parts and imaginary parts are equal. Thus if we have so , not a positive number. If we have so so or , again violating the givens. is equivalent to and , which are true if and only if so either or . Thus .
See Also
Mock AIME 2 2006-2007 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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