Difference between revisions of "1985 OIM Problems/Problem 5"

(Created page with "== Problem == To each positive integer <math>n</math> we assign an integer non-negative <math>f(n)</math> such that these conditions are satisfied: (i) <math>f(rs)=f(r)+f(s)<...")
 
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Find <math>f(1985)</math>. Justify your answer.
 
Find <math>f(1985)</math>. Justify your answer.
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~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
  
 
== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
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== See also ==
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https://www.oma.org.ar/enunciados/ibe1.htm

Revision as of 12:25, 13 December 2023

Problem

To each positive integer $n$ we assign an integer non-negative $f(n)$ such that these conditions are satisfied:

(i) $f(rs)=f(r)+f(s)$

(ii) $f(n)=0$, when the unit digit of $n$ is 3

(iii) $f(10)=0$

Find $f(1985)$. Justify your answer.

~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.

See also

https://www.oma.org.ar/enunciados/ibe1.htm