Difference between revisions of "2002 AIME I Problems/Problem 4"
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<math>\dfrac{n-m}{mn}=\dfrac{1}{29}</math> | <math>\dfrac{n-m}{mn}=\dfrac{1}{29}</math> | ||
− | Since we need a 29 in the denominator, let <math> | + | Since we need a 29 in the denominator, let <math>n=29t</math>.* Substituting, |
<math>29t-m=mt</math> | <math>29t-m=mt</math> |
Revision as of 23:53, 9 November 2010
Problem
Consider the sequence defined by for . Given that , for positive integers and with , find .
Solution
. Thus,
Which is
Since we need a 29 in the denominator, let .* Substituting,
Since n is an integer, , or . It quickly follows that and , so .
- If , a similar argument to the one above implies and , which implies , which is impossible since .
See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |