ProblemIdownloadedatexfilefromarxiv,itstartswith\inputamstex\documentstyle{amsppt}\magnification=1200\hsize=13.8cm\catcode`\@=11\def\NoLogo{\let\logo@\empty}\catcode`\@=\active\NoLogo\def\vgk{\text{\bfVG}_k}\def\