1988 IMO Problems/Problem 3: Difference between revisions
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A function <math>f</math> is defined on the positive integers by | A function <math>f</math> is defined on the positive integers by | ||
<math> f(1) = 1, f(3) = 3, f (2n) = f (n)</math> , | <math> f(1) = 1, f(3) = 3, f (2n) = f (n)</math> , | ||
<math> f(4n+1) = 2f(2n+1)−f(n), f(4n+3) = 3f(2n+1)−2f(n)</math> , | <math> f(4n+1) = 2f(2n+1)−f(n)</math>, <math>f(4n+3) = 3f(2n+1)−2f(n)</math> , | ||
for all positive integers <math> n</math> . | for all positive integers <math> n</math> . | ||
Determine the number of positive integers <math> n</math> , less than or equal to <math> 1988</math> , for which <math> f(n) = n</math> | Determine the number of positive integers <math> n</math> , less than or equal to <math> 1988</math> , for which <math> f(n) = n</math> | ||
. | . | ||
Revision as of 13:22, 7 June 2019
A function 
is defined on the positive integers by
,
$f(4n+1) = 2f(2n+1)−f(n)$ (Error compiling LaTeX. Unknown error_msg), $f(4n+3) = 3f(2n+1)−2f(n)$ (Error compiling LaTeX. Unknown error_msg) ,
for all positive integers 
.
Determine the number of positive integers , less than or equal to 
, for which 
.
