Ivan Shishkin, Rye (1878)

Problems/Arithmetic

Une équation fonctionnelle itérative

by YakYok·
34
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
ReviewedReviewed by Ancient Tree
·
Français
FrançaisAdd translation

Showing the Français version because no English translation exists yet. Add that translation.

Déterminer les fonctions f:N→Nf:\mathbb{N}\to\mathbb{N} telles que :
f(0)=0,f(n)>0  pour tout n>0f(0)=0, \quad f(n)>0 \:\text{ pour tout }n>0et, pour tous m,n∈Nm,n\in\mathbb{N},
f(mn)=f(m)f(n),f(f(n))n=f(n)f(n).f(mn)=f(m)f(n), \qquad f(f(n))^n=f(n)^{f(n)}.On adopte la convention 00=10^0=1.

I solved itMark it doneAdd to my listKeep it in your list
I like this problem2 likes

Liked by

Show related problems0

No related problems yet.

Solutions

0
Report

For an unclear, ambiguous, or possibly incorrect statement, please use the Discussion tab on the right. Report content that needs moderator intervention, such as dangerous, clearly non-mathematical, or plagiarized content.