MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - First Round
1992 Poland - First Round
4
Functional equation
Functional equation
Source: Poland Math Olympiad 1992 First Round #4
June 2, 2023
function
algebra
functional equation
Problem Statement
Determine all functions
f
:
R
⟶
R
f: R \longrightarrow R
f
:
R
⟶
R
such that
f
(
x
+
y
)
−
f
(
x
−
y
)
=
f
(
x
)
∗
f
(
y
)
f(x+y)-f(x-y)=f(x)*f(y)
f
(
x
+
y
)
−
f
(
x
−
y
)
=
f
(
x
)
∗
f
(
y
)
for
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
Back to Problems
View on AoPS