MathDB

Integer function

Source: Serbia TST 2017 #3

May 21, 2017

functionalgebra

Problem Statement

A function

f:\mathbb{N} \rightarrow \mathbb{N}

is called nice if

f^a(b)=f(a+b-1)

, where

f^a(b)

denotes

a

times applied function

f

. Let

g

be a nice function, and an integer

A

exists such that

g(A+2018)=g(A)+1

. a) Prove that

g(n+2017^{2017})=g(n)

for all

n \geq A+2

. b) If

g(A+1) \neq g(A+1+2017^{2017})

find

g(n)

for

n <A

.

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