Difference between revisions of "1993 OIM Problems/Problem 3"
(Created page with "== Problem == Let <math>N*={1,2,3,\cdots }</math>. Find all functions <math>f: N* \to N*</math> such that: i. If <math>x < y</math> then <math>f(x) < f(y)</math> ii. <math>f...") |
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== Problem == | == Problem == | ||
| − | Let <math>N*={1,2,3,\cdots }</math>. Find all functions <math>f: N* \to N*</math> such that: | + | Let <math>N^*={1,2,3,\cdots }</math>. Find all functions <math>f: N^* \to N^*</math> such that: |
i. If <math>x < y</math> then <math>f(x) < f(y)</math> | i. If <math>x < y</math> then <math>f(x) < f(y)</math> | ||
| − | ii. <math>f(y(f(x)) = x^2 f(xy)</math>, for all <math>x</math>, and <math>y</math> in <math>N*</math>. | + | ii. <math>f(y(f(x)) = x^2 f(xy)</math>, for all <math>x</math>, and <math>y</math> in <math>N^*</math>. |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 13:15, 13 December 2023
Problem
Let 
. Find all functions 
such that:
i. If 
then 
ii. 
, for all 
, and 
in 
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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