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Austrian-Polish
1982 Austrian-Polish Competition
6
6
Part of
1982 Austrian-Polish Competition
Problems
(1)
f(x+y) = f (x) f (y) for all x,y >= a with x + y >= a.
Source: Austrian Polish 1982 APMC
4/30/2020
An integer
a
a
a
is given. Find all real-valued functions
f
(
x
)
f (x)
f
(
x
)
defined on integers
x
≥
a
x \ge a
x
≥
a
, satisfying the equation
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f (x+y) = f (x) f (y)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all
x
,
y
≥
a
x,y \ge a
x
,
y
≥
a
with
x
+
y
≥
a
x + y \ge a
x
+
y
≥
a
.
functional
functional equation
algebra