% Format: Lollipop \DefineHeading:Chapter breakbefore:yes whiteafter:12pt line:start PointSize:20 Style:bold literal:Chapter Spaces:1 ChapterCounter line:stop vwhite:36pt line:start PointSize:24 Style:bold title line:stop vwhite:24pt Stop \DefineHeading:Section whitebefore:{20pt plus 2pt} whiteafter:14pt line:start PointSize:14 Style:bold ChapterCounter . SectionCounter Spaces:1 title line:stop label:start ChapterCounter . SectionCounter label:stop Stop \GoverningCounter:Section=Chapter \AlwaysIndent:no \Distance:parskip=12pt \Distance:hoffset=.75in \Distance:voffset=.5in \Start \Chapter Unsolved Problems \Section Odd Perfect Numbers 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. \Stop