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Belarus Contests
Belarus Team Selection Test
2019 Belarus Team Selection Test
8.2
8.2
Part of
2019 Belarus Team Selection Test
Problems
(1)
FE in integers
Source: 2019 Belarus Team Selection Test 8.2
9/2/2019
Let
Z
\mathbb Z
Z
be the set of all integers. Find all functions
f
:
Z
→
Z
f:\mathbb Z\to\mathbb Z
f
:
Z
→
Z
satisfying the following conditions: 1.
f
(
f
(
x
)
)
=
x
f
(
x
)
−
x
2
+
2
f(f(x))=xf(x)-x^2+2
f
(
f
(
x
))
=
x
f
(
x
)
−
x
2
+
2
for all
x
∈
Z
x\in\mathbb Z
x
∈
Z
; 2.
f
f
f
takes all integer values.(I. Voronovich)
algebra
functional equation
function