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Rioplatense Mathematical Olympiad, Level 3
2023 Rioplatense Mathematical Olympiad
6
FE today, FE tomorrow, FE...
FE today, FE tomorrow, FE...
Source: Rioplatense L2 2023 #6
December 6, 2023
algebra
function
Problem Statement
Find all functions
f
:
Z
ā
Z
f:\mathbb{Z} \rightarrow \mathbb{Z}
f
:
Z
ā
Z
such that
f
(
x
+
f
(
y
+
1
)
)
+
f
(
x
y
)
=
f
(
x
+
1
)
(
f
(
y
)
+
1
)
f(x+f(y+1))+f(xy)=f(x+1)(f(y)+1)
f
(
x
+
f
(
y
+
1
))
+
f
(
x
y
)
=
f
(
x
+
1
)
(
f
(
y
)
+
1
)
for any
x
,
y
x,y
x
,
y
integers.
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