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Latvia BW TST
2017 Latvia Baltic Way TST
3
f(x+y)+f(xy)=f(x)f(y)+1 in Z
f(x+y)+f(xy)=f(x)f(y)+1 in Z
Source: 2017 Latvia BW TST P3
December 18, 2022
algebra
functional equation
Problem Statement
Find all functions
f
(
x
)
:
Z
→
Z
f (x) : Z \to Z
f
(
x
)
:
Z
→
Z
defined on integers, take integer values, and for all
x
,
y
∈
Z
x,y \in Z
x
,
y
∈
Z
satisfy
f
(
x
+
y
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
1
f(x+y)+f(xy)=f(x)f(y)+1
f
(
x
+
y
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
1
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