Difference between revisions of "2010 OIM Problems/Problem 2"
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== Problem == | == Problem == | ||
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Find if there are positive integers <math>a</math> and <math>b</math> such that all terms of the sequence defined by | Find if there are positive integers <math>a</math> and <math>b</math> such that all terms of the sequence defined by | ||
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== Solution == | == Solution == | ||
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{{solution}} | {{solution}} | ||
| − | == See | + | == See Also == |
| − | [[OIM Problems and Solutions]] | + | * [[OIM Problems and Solutions]] |
Latest revision as of 09:52, 25 February 2025
Problem
Find if there are positive integers 
and 
such that all terms of the sequence defined by
![\[x_1 = 2010,\; x_2 = 2011,\;x_{n+2}=x_n+x_{n+1}+a\sqrt{x_nx_{n+1}+b},\;n \ge 1,\]](http://latex.artofproblemsolving.com/9/2/2/92242436602a0b73fae868ae3f77774fa29c9d0e.png)
be integers.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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