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2018 JBMO Shortlist
A2
m^3+n^3>(m+n)^2
m^3+n^3>(m+n)^2
Source: JBMO shortlist 2018, A2
June 23, 2019
algebra
Problem Statement
Find the maximum positive integer
k
k
k
such that for any positive integers
m
,
n
m,n
m
,
n
such that
m
3
+
n
3
>
(
m
+
n
)
2
m^3+n^3>(m+n)^2
m
3
+
n
3
>
(
m
+
n
)
2
, we have
m
3
+
n
3
≥
(
m
+
n
)
2
+
k
m^3+n^3\geq (m+n)^2+k
m
3
+
n
3
≥
(
m
+
n
)
2
+
k
Proposed by Dorlir Ahmeti, Albania
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