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Baltic Way
1996 Baltic Way
13
13
Part of
1996 Baltic Way
Problems
(1)
f(x)=f(x^2+x+1) when f is either odd or even
Source: Baltic Way 1996 Q13
3/19/2011
Consider the functions
f
f
f
defined on the set of integers such that
f
(
x
)
=
f
(
x
2
+
x
+
1
)
f(x)=f(x^2+x+1)
f
(
x
)
=
f
(
x
2
+
x
+
1
)
for all integer
x
x
x
. Find
(
a
)
(a)
(
a
)
all even functions,
(
b
)
(b)
(
b
)
all odd functions of this kind.
function
algebra proposed
algebra