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Vojtěch Jarník IMC
2000 VJIMC
Problem 3
Czech Republic 2000
Czech Republic 2000
Source:
June 6, 2015
inequalities
function
Problem Statement
Prove that if m,n are nonnegative integers and 0<=x<=1 then
(
1
−
x
n
)
m
+
(
1
−
(
1
−
x
)
m
)
n
≥
1
(1-x^n)^m + (1-(1-x)^m)^n \ge 1
(
1
−
x
n
)
m
+
(
1
−
(
1
−
x
)
m
)
n
≥
1
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