% Format: Plain \font\chapfont=cmbx12 scaled 1728 \font\titlefont=cmbx12 scaled 2073 \font\secfont=cmbx12 scaled 1200 \parskip=\baselineskip \parindent=0pt \hsize=5in \hoffset=.75in \leftline{\chapfont Chapter 1} \vskip36pt \leftline{\titlefont Unsolved Problems} \vskip36pt \leftline{\secfont 1.1\ \ Odd Perfect Numbers} \vskip12pt A number is said to be {\it perfect\/} if it is the sum of its divisors. For example, $6$ is perfect because $1+2+3 = 6$, and $1$, $2$, and $3$ are the only numbers that divide evenly into $6$ (apart from $6$ itself). It has been shown that all even perfect numbers have the form $$2^{p-1}(2^{p}-1)$$ where $p$ and $2^{p}-1$ are both prime. The existence of {\it odd\/} perfect numbers is an open question. \bye