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1993 USAMO Problems/Problem 4

Revision as of 19:32, 22 April 2010 by Moplam (talk | contribs) (Created page with '== Problem 4== Let <math>a</math>, <math>b</math> be odd positive integers. Define the sequence <math>(f_n)</math> by putting <math>f_1 = a</math>, <math>f_2 = b</math>, and by …')
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Problem 4

Let $a$, $b$ be odd positive integers. Define the sequence $(f_n)$ by putting $f_1 = a$, $f_2 = b$, and by letting fn for $n\ge3$ be the greatest odd divisor of $f_{n-1} + f_{n-2}$. Show that $f_n$ is constant for $n$ sufficiently large and determine the eventual value as a function of $a$ and $b$.


Solution

Being typed up now ^v^- 07:32 PM EDT 4/22

Resources

1993 USAMO (Problems • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions
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