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CentroAmerican
2003 CentroAmerican
3
3
Part of
2003 CentroAmerican
Problems
(1)
Exponential inequality for integers a,b
Source: CentroAmerican 2003
11/29/2010
Let
a
a
a
and
b
b
b
be positive integers with
a
>
1
a>1
a
>
1
and
b
>
2
b>2
b
>
2
. Prove that
a
b
+
1
≥
b
(
a
+
1
)
a^b+1\ge b(a+1)
a
b
+
1
≥
b
(
a
+
1
)
and determine when there is inequality.
inequalities
calculus
logarithms
induction
inequalities proposed