My Math Forum Solutions for 2^(-a)+2^(-b)=1

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 February 10th, 2014, 11:57 AM #1 Newbie   Joined: Feb 2014 Posts: 1 Thanks: 0 Solutions for 2^(-a)+2^(-b)=1 Equation $2^{-a}+2^{-b}=1$ has solution $a=b=1$. Are there other solutions when $a$ and $b$ shall be rational? My guess is no but I don't know how to prove it.
 February 10th, 2014, 01:58 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Solutions for 2^(-a)+2^(-b)=1 Perhaps of interest: $2^{-a}\,+\,2^{-b}\,=\,1\,\Rightarrow\,2^a\,+\,2^b\,=\,2^{a+b}$ $n\,\cdot\,n^{\frac{1}{n-1}}\,=\,n^{\frac{n}{n-1}},\,n\,\in\,\mathbb{N},\,n\,>\,1=$

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