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National and Regional Contests
Turkey Contests
Turkey Junior National Olympiad
2000 Turkey Junior National Olympiad
3
3
Part of
2000 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 2000, Part II - P3
Source:
1/18/2013
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
satisfies the equation
f
(
x
)
f
(
y
)
−
a
f
(
x
y
)
=
x
+
y
f(x)f(y)-af(xy)=x+y
f
(
x
)
f
(
y
)
−
a
f
(
x
y
)
=
x
+
y
, for every real numbers
x
,
y
x,y
x
,
y
. Find all possible real values of
a
a
a
.
algebra
polynomial