This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.1.10) 27 JAN 2010 12:18 entering extended mode %&-line parsing enabled. **hw3-soln (./hw3-soln.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, ukrainian, russian, bulgarian, loaded. (/usr/share/texmf-texlive/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size11.clo File: size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) \@input{macros.aux} \openout2 = `macros.aux'. (./macros.tex (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. (/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 (/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen103 )) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen104 ) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count87 LaTeX Info: Redefining \frac on input line 211. \uproot@=\count88 \leftroot@=\count89 LaTeX Info: Redefining \overline on input line 307. \classnum@=\count90 \DOTSCASE@=\count91 LaTeX Info: Redefining \ldots on input line 379. LaTeX Info: Redefining \dots on input line 382. LaTeX Info: Redefining \cdots on input line 467. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen105 LaTeX Font Info: Redeclaring font encoding OML on input line 567. LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \macc@depth=\count92 \c@MaxMatrixCols=\count93 \dotsspace@=\muskip10 \c@parentequation=\count94 \dspbrk@lvl=\count95 \tag@help=\toks15 \row@=\count96 \column@=\count97 \maxfields@=\count98 \andhelp@=\toks16 \eqnshift@=\dimen106 \alignsep@=\dimen107 \tagshift@=\dimen108 \tagwidth@=\dimen109 \totwidth@=\dimen110 \lineht@=\dimen111 \@envbody=\toks17 \multlinegap=\skip44 \multlinetaggap=\skip45 \mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. ) (/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2001/10/25 v2.2f \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. ) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty Package: amssymb 2002/01/22 v2.2d ) (/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty Package: amsthm 2004/08/06 v2.20 \thm@style=\toks19 \thm@bodyfont=\toks20 \thm@headfont=\toks21 \thm@notefont=\toks22 \thm@headpunct=\toks23 \thm@preskip=\skip46 \thm@postskip=\skip47 \thm@headsep=\skip48 \dth@everypar=\toks24 ) (/usr/share/texmf-texlive/tex/latex/tools/xspace.sty Package: xspace 2006/05/08 v1.12 Space after command names (DPC,MH) ) \c@theorem=\count99 \c@listnum=\count100 ) (./hw3-soln.aux) \openout1 = `hw3-soln.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 7. LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 7. LaTeX Font Info: Try loading font information for OT2+cmr on input line 7. (/usr/share/texmf-texlive/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 2001/08/11 v3.2c Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 7. LaTeX Font Info: Try loading font information for U+msa on input line 8. (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 8. (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) Overfull \hbox (81.28058pt too wide) in paragraph at lines 34--34 []\OT1/cmtt/m/n/10.95 sage: def f(n): return prod([Mod(a,n) for a in [1..n] if gcd(a,n) == 1])[] [] [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (6.54764pt too wide) in paragraph at lines 98--98 [] \OT1/cmtt/m/n/10.95 sage: x = (Mod(2010,2011) - Mod(7,2011))/Mod(5,2011) ; x[] [] [2] [3] (./hw3-soln.aux) ) Here is how much of TeX's memory you used: 1682 strings out of 94834 16763 string characters out of 1179181 64983 words of memory out of 1500000 4886 multiletter control sequences out of 10000+50000 12617 words of font info for 49 fonts, out of 1200000 for 2000 212 hyphenation exceptions out of 8191 31i,6n,24p,238b,401s stack positions out of 5000i,500n,6000p,200000b,5000s Output written on hw3-soln.pdf (3 pages, 70633 bytes). PDF statistics: 64 PDF objects out of 1000 (max. 8388607) 0 named destinations out of 1000 (max. 131072) 1 words of extra memory for PDF output out of 10000 (max. 10000000)