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2021-IMOC
A8
Nice natural FE with an inequality
Nice natural FE with an inequality
Source: IMOC 2021 A8
August 11, 2021
functional equation
algebra
Inequality
function
inequalities
Problem Statement
Find all functions
f
:
N
ā
N
f : \mathbb{N} \to \mathbb{N}
f
:
N
ā
N
with
f
(
x
)
+
y
f
(
f
(
x
)
)
<
x
(
1
+
f
(
y
)
)
+
2021
f(x) + yf(f(x)) < x(1 + f(y)) + 2021
f
(
x
)
+
y
f
(
f
(
x
))
<
x
(
1
+
f
(
y
))
+
2021
holds for all positive integers
x
,
y
.
x,y.
x
,
y
.
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