# LaTeX2HTML 95 (Thu Jan 19 1995)
# Associate image original text (scrambled) with physical files.
$key = q/{_inline}$df(t)leB${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=t+3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$S_5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x+n-1choosen-1>.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi=16037425${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$x^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$T(0)=0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$t=2,,5,,6,,7${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$[3]${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)-t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$de_n(k)=natopwithdelimslangleranglek${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}a_t+tequivdf(t)+tequivpi_f(t)bmodn{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}${a,a+1,ldots,b}${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$G(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$S_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(1)=1+df(1)=6=2+df(2)=f(2){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(x)~=~casesx+4;SPM_amp;if$xequiv0,~1bmod3$crx+1;SPM_amp;if$xequiv2bmod3$cr{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)ge0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}I={a,a+1,ldots,b}~subset~bfZ.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$fcolonbfZtoZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}pi(0)pi(1)ldotspi(n-1).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(t)=pi_f(t)+ncdotg(t)=pi(t)+ncdotg(t),qquad0let;SPM_lt;n.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$ldots5,1,5,1,ldots${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}(b+1)^n-b^n~=~sum_d|n~dM(d,b).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}x^n=sum_k=0^n-1natopwithdelimslangleranglekx+kchoosen.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$piinS_8${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$[n-1]${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t):=f(t)-t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$Z${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{figure}picture(5,5)picture{figure}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$uinZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t+n)=df(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi_f=pi${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}B(f)=1overnsum_t=0^n-1,df(t)=1overnsum_t=0^n-1,bigl(pi(t)-t+ncdotg(t)bigr).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$t=0,1,ldots,n-1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}df(t)=f(t)-t=pi_f(t)-t+ncdotg(t){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}N_;SPM_lt;(b,n)=b^n.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$M(n,b)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=f(u)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}N(b,n)=sum_k=0^n-1de_n(k)pmatrixn+b-k-1crn-1.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)-1.5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}df(t)=pi(t)-t+ncdotg(t){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$b^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$qed${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)=f(t)-t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$tinZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$de_n(k)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$tinbfZ:={ldots,-2,-1,0,1,2,ldots}${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_t+t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$tin[n]${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(2)=4${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$tinI${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$x+kchoosen${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(4+4+1)3=3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$t'${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=a_t+t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=a_t+t=f(u)=a_u+u${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)=a_t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$iin[n]${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$B(f)=b${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$ttot+3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi(i)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$t+a_tbmodn${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}a_0a_1cdotsa_n-1{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)equivpi_f(t)bmodn${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}B(f)=sum_t=0^n-1g(t).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}lim_|I|rightarrowinfty~sum_xinIdf(x)over|I|{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pih${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$hatpi=36201754${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}de_n(k)=natopwithdelimslangleranglek.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=t+2cdotT(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$N(b,n)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}natopwithdelimslangleranglek{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$i=1,,2,,5,,6${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(1)=5${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}N_;SPM_lt;(b,n)=sum_k=0^n-1de_n(k)~pmatrixn+b-k-1crncr=sum_k=0^n-1natopwithdelimslangleranglekn+b-k-1choosen.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$gcolon[n]toZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)get${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$G(t)=g(t)-d_pi(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$g(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t')=u${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}sequivtbmodn~~Longrightarrow~~f(s)equivf(t)bmodn.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=t+a_{t}equivubmodn${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}N_;SPM_lt;(b,n)=sum_k=0^n-1natopwithdelimslangleranglek~pmatrixb+kcrncr.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=pi_f(t)+ncdotg(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$(b+1)^n-b^n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$T(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_t+tbmodn${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=t+df(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(t)=pi(t)+ncdotd_pi(t)+ncdotG(t).{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$ep${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(x)=x+4${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}${0,1,ldots,n-1}${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$tequivubmodn${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$B(f)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)=3${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi(t);SPM_lt;t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$t+df(t)=f(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$piinS_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$[n]${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f:bfZrightarrowZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}${4n+a:ninbfZ}${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$f(t)=t${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$df(t)=0${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$0leqi;SPM_lt;n-1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_t=df(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi(i);SPM_gt;pi(i+1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_0a_1cdotsa_n-1${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(x)~=~casesy;SPM_amp;iftheballthrownattime$x$isnextthrownattime$y$crx;SPM_amp;ifthereisnothrowattime$x$.cr{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi(t)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}f(t)equivpi_f(t)bmodn,qquad1letlen.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$inZ${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}d_pi(t)~=~cases1;SPM_amp;if$t$isadropfor$pi$cr0;SPM_amp;if$t$isnotadropfor$pi$.cr{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi~=~pi(0)pi(1)ldotspi(n-1)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$N_;SPM_lt;(b,n)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi_finS_n${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$a_t=a_u${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$pi'~=~pi(n-1)pi(n-2)ldotspi(0)${_inline}/;
$cached_env_img{$key} ='
';
$key = q/{_inline}$3^rmrd${_inline}/;
$cached_env_img{$key} ='
';
1;