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2020 Japan MO Finals
3
Japan MO Finals 2020-3
Japan MO Finals 2020-3
Source: Japan MO Finals 2020-3
February 11, 2020
Japan
function
Problem Statement
Find all functions
f
:
Z
+
→
Z
+
f:\mathbb{Z}^{+}\to\mathbb{Z}^{+}
f
:
Z
+
→
Z
+
such that
m
2
+
f
(
n
)
2
+
(
m
−
f
(
n
)
)
2
≥
f
(
m
)
2
+
n
2
m^{2}+f(n)^{2}+(m-f(n))^{2}\geq f(m)^{2}+n^{2}
m
2
+
f
(
n
)
2
+
(
m
−
f
(
n
)
)
2
≥
f
(
m
)
2
+
n
2
for all pairs of positive integers
(
m
,
n
)
(m,n)
(
m
,
n
)
.
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