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2017-IMOC
A5
A5
Part of
2017-IMOC
Problems
(1)
FE over Z
Source: IMOC 2017 A5
8/12/2021
Find all functions
f
:
Z
ā
Z
f:\mathbb Z\to\mathbb Z
f
:
Z
ā
Z
such that
f
(
m
f
(
n
+
1
)
)
=
f
(
m
+
1
)
f
(
n
)
+
f
(
f
(
n
)
)
+
1
f(mf(n+1))=f(m+1)f(n)+f(f(n))+1
f
(
m
f
(
n
+
1
))
=
f
(
m
+
1
)
f
(
n
)
+
f
(
f
(
n
))
+
1
for all integer pairs
(
m
,
n
)
(m,n)
(
m
,
n
)
.
fe
functional equation
algebra