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## Problem of the Day #252: Lower Bound on Alex NumbersNovember 26, 2011

Posted by Saketh in : potd , trackback

We define the Alex number $A(a,b)$ to be to greatest real value $R$ for which $x^y + y^x \gt R$ for all $x,y$ such that $0 \lt x \lt a$ and $0 \lt y \lt b$. Find, with proof, an expression for $A(a,b)$ in terms of $a$ and $b$.

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