MathDB

Function

f: R\to R

is said periodic , if

f

is not a constant function and there is a number real positive

p

with the property of

f (x) = f (x + p)

for every

x \in R

. The smallest positive real number p which satisfies the condition

f (x) = f (x + p)

for each

x \in R

is named period of

f

. Given

a

and

b

real positive numbers, show that there are periodic functions

f_1

and

f_2

, with periods

a

and

b

respectively, so that

f_1 (x)\cdot f_2 (x)

is also a periodic function.

Problem Statement