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1980 IMO Shortlist
7
7
Part of
1980 IMO Shortlist
Problems
(1)
f(xy) = f(x)f(y) - f(x+y) + 1
Source: IMO 1980 Luxembourg, problem 1
5/6/2004
The function
f
f
f
is defined on the set
Q
\mathbb{Q}
Q
of all rational numbers and has values in
Q
\mathbb{Q}
Q
. It satisfies the conditions
f
(
1
)
=
2
f(1) = 2
f
(
1
)
=
2
and
f
(
x
y
)
=
f
(
x
)
f
(
y
)
−
f
(
x
+
y
)
+
1
f(xy) = f(x)f(y) - f(x+y) + 1
f
(
x
y
)
=
f
(
x
)
f
(
y
)
−
f
(
x
+
y
)
+
1
for all
x
,
y
∈
Q
x,y \in \mathbb{Q}
x
,
y
∈
Q
. Determine
f
f
f
.
function
algebra
functional equation
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