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50
Inequality for integers m,n [ILL 1974]
Inequality for integers m,n [ILL 1974]
Source:
January 3, 2011
inequalities
inequalities proposed
Problem Statement
Let
m
m
m
and
n
n
n
be natural numbers with
m
>
n
m>n
m
>
n
. Prove that
2
(
m
−
n
)
2
(
m
2
−
n
2
+
1
)
≥
2
m
2
−
2
m
n
+
1
2(m-n)^2(m^2-n^2+1)\ge 2m^2-2mn+1
2
(
m
−
n
)
2
(
m
2
−
n
2
+
1
)
≥
2
m
2
−
2
mn
+
1
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