MathDB
Problems
Contests
International Contests
Tuymaada Olympiad
1995 Tuymaada Olympiad
7
f(x)-f(ax)=x^n-x^m where n,m\in N , 0<a<1
f(x)-f(ax)=x^n-x^m where n,m\in N , 0<a<1
Source: Tuymaada 1995 p7
April 27, 2019
functional equation
algebra
continuous function
Problem Statement
Find a continuous function
f
(
x
)
f(x)
f
(
x
)
satisfying the identity
f
(
x
)
−
f
(
a
x
)
=
x
n
−
x
m
f(x)-f(ax)=x^n-x^m
f
(
x
)
−
f
(
a
x
)
=
x
n
−
x
m
, where
n
,
m
∈
N
,
0
<
a
<
1
n,m\in N , 0<a<1
n
,
m
∈
N
,
0
<
a
<
1
Back to Problems
View on AoPS