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Bulgaria National Olympiad
2021 Bulgaria National Olympiad
3
3
Part of
2021 Bulgaria National Olympiad
Problems
(1)
f(f(x) + y)f(x) = f(xy + 1)
Source: IMOC 2020 A2
8/31/2020
Find all
f
:
R
+
→
R
+
f:R^+ \rightarrow R^+
f
:
R
+
→
R
+
such that
f
(
f
(
x
)
+
y
)
f
(
x
)
=
f
(
x
y
+
1
)
∀
x
,
y
∈
R
+
f(f(x) + y)f(x) = f(xy + 1)\ \ \forall x, y \in R^+
f
(
f
(
x
)
+
y
)
f
(
x
)
=
f
(
x
y
+
1
)
∀
x
,
y
∈
R
+
@below: https://artofproblemsolving.com/community/c6h2254883_2020_imoc_problemsFeel free to start individual threads for the problems as usual
functional equation
algebra
IMOC