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Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2017 Canadian Mathematical Olympiad Qualification
3
3
Part of
2017 Canadian Mathematical Olympiad Qualification
Problems
(1)
Functional equation: sum, difference, difference of squares
Source: Canada Repêchage 2017/3
4/13/2017
Determine all functions
f
:
R
→
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
that satisfy the following equation for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
.
(
x
+
y
)
f
(
x
−
y
)
=
f
(
x
2
−
y
2
)
.
(x+y)f(x-y) = f(x^2-y^2).
(
x
+
y
)
f
(
x
−
y
)
=
f
(
x
2
−
y
2
)
.
algebra
functional equation
function
difference of squares
special factorizations