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Cute inequality with integers

Source: Central American Olympiad 2003, Problem 3

May 23, 2007
inequalitiesinductionfunctioncalculus

Problem Statement

If a>1a>1 and b>2b>2 are positive integers, show that ab+1≥b(a+1)a^{b}+1 \geq b(a+1), and determine when equality holds.
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