MathDB

Period of function (Izho)

Source: Izho

January 12, 2019

number theory

Problem Statement

Natural number

n>1

is given. Let

I

be a set of integers that are relatively prime to

n

. Define the function

f:I=>N

. We call a function

k-periodic

if for any

a,b

,

f(a)=f(b)

whenever

k|a-b

. We know that

f

is

n-periodic

. Prove that minimal period of

f

divides all other periods. Example: if

n=6

and

f(1)=f(5)

then minimal period is 1, if

f(1)

is not equal to

f(5)

then minimal period is 3.

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