Difference between revisions of "2009 OIM Problems/Problem 5"
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== Problem == | == Problem == | ||
| − | The sequence <math>a_n</math> is defined by <math>a_1 = 1, a_{2k} = 1 + a_k</math>, and <math>a_{2k+1} = \frac{1}{a_{2k}}, for all integer < | + | The sequence <math>a_n</math> is defined by <math>a_1 = 1, a_{2k} = 1 + a_k</math>, and <math>a_{2k+1} = \frac{1}{a_{2k}}</math>, for all integer <math>k \ge 1</math>. Prove that every positive rational number appears exactly once in this sequence. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 15:24, 14 December 2023
Problem
The sequence 
is defined by 
, and 
, for all integer 
. Prove that every positive rational number appears exactly once in this sequence.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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