MathDB
Problems
Contests
International Contests
International Mathematical Olympic Revenge
2018 International Olympic Revenge
4
Problem 4 IMOR 2018
Problem 4 IMOR 2018
Source: 2nd IMOR - 2018
July 13, 2018
IMOR
algebra
functional equation
Problem Statement
Find all functions
f
:
Q
→
R
f:\mathbb{Q}\rightarrow\mathbb{R}
f
:
Q
→
R
such that
f
(
x
)
2
−
f
(
y
)
2
=
f
(
x
+
y
)
⋅
f
(
x
−
y
)
,
f(x)^2-f(y)^2=f(x+y)\cdot f(x-y),
f
(
x
)
2
−
f
(
y
)
2
=
f
(
x
+
y
)
⋅
f
(
x
−
y
)
,
for all
x
,
y
∈
Q
x,y\in \mathbb{Q}
x
,
y
∈
Q
.Proposed by Portugal.
Back to Problems
View on AoPS