This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2000.7.19) 29 JAN 2002 13:27 **solnfinal.tex (solnfinal.tex LaTeX2e <1999/12/01> patch level 1 Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 1999/09/10 v1.4a Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size10.clo File: size10.clo 1999/09/10 v1.4a 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/tex/latex/amsmath/amsmath.sty Package: amsmath 2000/01/15 v2.05 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 1999/11/15 v2.0 (/usr/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen103 )) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen104 ) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count87 LaTeX Info: Redefining \frac on input line 198. \uproot@=\count88 \leftroot@=\count89 LaTeX Info: Redefining \overline on input line 302. \classnum@=\count90 \DOTSCASE@=\count91 LaTeX Info: Redefining \ldots on input line 376. LaTeX Info: Redefining \dots on input line 379. LaTeX Info: Redefining \cdots on input line 464. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen105 LaTeX Font Info: Redeclaring font encoding OML on input line 563. 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LaTeX Info: Redefining \] on input line 2595. ) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \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 133. ) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b ) (/usr/share/texmf/tex/latex/amscls/amsthm.sty Package: amsthm 2000/01/17 v2.03 \thm@style=\toks18 \thm@bodyfont=\toks19 \thm@headfont=\toks20 \thm@notefont=\toks21 \thm@headpunct=\toks22 \thm@preskip=\skip46 \thm@postskip=\skip47 \thm@headsep=\skip48 \dth@everypar=\toks23 ) \c@theorem=\count98 \c@listnum=\count99 ) \c@theprob=\count100 \c@thesubprob=\count101 (solnfinal.aux) \openout1 = `solnfinal.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OT2/cmr/m/n on input line 12. LaTeX Font Info: Try loading font information for OT2+cmr on input line 12. (/usr/share/texmf/tex/latex/cyrillic/ot2cmr.fd File: ot2cmr.fd 1999/06/24 v3.2b Computer Modern Cyrillic font definitions ) LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Try loading font information for U+msa on input line 13. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 13. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] Overfull \hbox (2.37674pt too wide) in paragraph at lines 134--141 \OT1/cmr/m/n/10 [3\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ] = 3 + (\OMS/cmsy/m/n/1 0 ^^@\OT1/cmr/m/n/10 2 + 2[]) = 1 + 2[]$. As a check, type \OT1/cmtt/m/n/10 con tfrac(1+2*sqrt(2)) [] [2] Overfull \hbox (3.495pt too wide) in paragraph at lines 244--244 []\OT1/cmtt/m/n/10 ? q*prod(n=1,30,(1-q^n)^2)*prod(n=1,3,(1-q^(11*n))^2) + O( q^30)[] [] Overfull \hbox (24.49481pt too wide) in paragraph at lines 244--244 []\OT1/cmtt/m/n/10 %22 = q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10[] [] Overfull \hbox (13.9949pt too wide) in paragraph at lines 244--244 [] \OT1/cmtt/m/n/10 + q^11 - 2*q^12 + 4*q^13 + 4*q^14 - q^15 - 4*q^16 - 2*q^17[] [] [3] Overfull \hbox (24.49481pt too wide) in paragraph at lines 244--244 [] \OT1/cmtt/m/n/10 + 4*q^18 + 2*q^20 + 2*q^21 - 2*q^22 - q^23 - 4*q^25 - 8*q^26[] [] Overfull \hbox (2.49481pt too wide) in paragraph at lines 294--294 [] \OT1/cmtt/m/n/10 ellpow(E,[0,1]*Mod(1,N),m); \\ this fails if and only i f we win![] [] Overfull \hbox (28.74458pt too wide) in paragraph at lines 303--303 [] \OT1/cmtt/m/n/10 *** impossible inverse modulo: Mod(495899, 124531325385 603661726997).[] [] [4] Overfull \hbox (28.74458pt too wide) in paragraph at lines 313--313 [] \OT1/cmtt/m/n/10 *** impossible inverse modulo: Mod(311221384171, 251122 356337890703).[] [] Overfull \hbox (12.99472pt too wide) in paragraph at lines 341--341 []\OT1/cmtt/m/n/10 %9 = [Mod(20641240315, 311221384171), Mod(200682828122, 311 221384171)][] [] [5] (solnfinal.aux) ) Here is how much of TeX's memory you used: 1540 strings out of 20898 14699 string characters out of 196686 65484 words of memory out of 350001 4490 multiletter control sequences out of 10000+15000 12023 words of font info for 47 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 1000 31i,12n,24p,243b,506s stack positions out of 1500i,100n,500p,50000b,4000s Output written on solnfinal.dvi (5 pages, 17912 bytes).