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Austrian-Polish
2002 Austrian-Polish Competition
7
7
Part of
2002 Austrian-Polish Competition
Problems
(1)
Periodic functions s.t. f(x^2y) = (f(x))^2f(y)
Source: 2002 Austrian-Polish, problem 7
9/23/2006
Find all real functions
f
f
f
definited on positive integers and satisying:(a)
f
(
x
+
22
)
=
f
(
x
)
f(x+22)=f(x)
f
(
x
+
22
)
=
f
(
x
)
,(b)
f
(
x
2
y
)
=
(
f
(
x
)
)
2
f
(
y
)
f\left(x^{2}y\right)=\left(f(x)\right)^{2}f(y)
f
(
x
2
y
)
=
(
f
(
x
)
)
2
f
(
y
)
for all positive integers
x
x
x
and
y
y
y
.
function
algebra unsolved
algebra
functional equation