Difference between revisions of "1988 AIME Problems/Problem 2"
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== Solution == | == Solution == | ||
We see that <math>f(11)=4</math> | We see that <math>f(11)=4</math> | ||
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<math>f(4)=16</math> | <math>f(4)=16</math> | ||
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<math>f(16)=49</math> | <math>f(16)=49</math> | ||
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<math>f(49)=169</math> | <math>f(49)=169</math> | ||
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<math>f(169)=256</math> | <math>f(169)=256</math> | ||
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<math>f(256)=169</math> | <math>f(256)=169</math> | ||
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Note that this revolves between the two numbers. | Note that this revolves between the two numbers. | ||
<math>f_{1984}(169)=169</math> | <math>f_{1984}(169)=169</math> |
Revision as of 13:53, 27 March 2007
Problem
For any positive integer , let
denote the square of the sum of the digits of
. For
, let
. Find
.
Solution
We see that
Note that this revolves between the two numbers.
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |