Difference between revisions of "1995 OIM Problems/Problem 6"

Latest revision as of 14:57, 13 December 2023

Problem

A function $f: N \to N$ is circular if for every $p$ in $N$ there exists $n$ in $N$ with $n \le p$ such that

$f^n(p) = f( f( \cdots \text{n times} \cdots f(p))) = p$

The function $f$ has degree of repulsion $k$ , $0 < k<1$ , if for each $p$ in $N$ , $f^i(p) \ne p$ for $i=1, 2, \cdots , \left\lfloor k.p \right\rfloor$ (*).

Find the greatest degree of repulsion that a circular function can have.

Note (*): $\left\lfloor x \right\rfloor$ indicates the largest integer less than or equal to $x$ .

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

@@ Line 4: / Line 4: @@
 <cmath>f^n(p) = f( f( \cdots \text{n times} \cdots f(p))) = p</cmath>
-The function f has degree of repulsion <math>k</math>, <math>0 < k<1</math>, if for each <math>p</math> in <math>N</math>, <math>f^i(p) \ne p</math> for <math>i=1, 2, \cdots , \left\lfloor k.p \right\rfloor</math> '''(*)'''.
+The function <math>f</math> has degree of repulsion <math>k</math>, <math>0 < k<1</math>, if for each <math>p</math> in <math>N</math>, <math>f^i(p) \ne p</math> for <math>i=1, 2, \cdots , \left\lfloor k.p \right\rfloor</math> '''(*)'''.
 Find the greatest degree of repulsion that a circular function can have.

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Difference between revisions of "1995 OIM Problems/Problem 6"

Latest revision as of 14:57, 13 December 2023

Problem

Solution

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