%% 428 \input style \subsubchap{ } , . 厒 . " " " " , : \medskip \item{i)} . \item{ii)} , , () . \medskip \noindent (ii), (i), . (i), (ii); , \picture{. 89. } . , , ; , - . . . , (i) (ii), %% 429 (. 89). , ; . " /" . , \emph{} \emph{}, / . --- , / , . , , \emph{}. , .~89 , / ; , , . 璎 , |MIXTEC|, $$ \eqalign{ \hbox{1 }& =\hbox{5000 ,}\cr \hbox{1 }& =\hbox{20 ,}\cr \hbox{1 }&= \hbox{200 .}\cr } $$   20 , . . , . , . , |MIXTEC|, , . , , , , : \itemize \li (, ). \li (, , / ). \li (, , ). \itemend |MIXTEC| $i$ $j$ $25+{1\over2}\vert i-j \vert$ . $i$ $j$--- 1 200, %%430 $\vert i-j\vert$ $2 \left( {201\atop 3}\right)/200^2\approx 66.7$, . . 60~. |MIXTEC| 25 , 12.5 . $n$ $(n/5000)\times25\hbox{ }=5n\hbox{ }$. (풎 $3{1\over3}$ , |MIXT|, .~5.4.6.)   , |MIXTEC| |MIXT|, , : \medskip \item{a)} . \item{b)} , , ( + ). \item{c)} ኎ . \medskip , (a). ⅏ --- , (b). \qsection ? . , , , /, . , - , . , , . "" . \enumerate \li , ( ) , . , / - . \li (.~90): , $A$, , , .. ${1\over2}\times25$ . , $B$, ${1\over 4}$ $1\over2$ ; %%431 ${3\over4}\times25$ . , $C$: , \emph{} $3\over4$ . , ${1\over2}\times25$ . , . , $C$. \picture{. 90. } , , + . ᐅ ${1\over2}(1-x^2)$ , $x$ ($0 , . .~5.4.4, , , . ("$T$-lifo" " $T$-fifo"), "" . \emph{ }, (. . ). ዅ, , , , $P$- , $P$--- , . (5.4.4--9) %% 434 $S$ () $$ qS-\lfloor(P^q-S)/(P-1)\rfloor, \qquad q=\lceil\log_P S\rceil. \eqno(1) $$ , $P$- . (., , .~91, $P=3$, $S=6$.) ፀ , , " ", $S\equiv1 \pmod{P-1}$; " --- \picture{. 92. ...} ", $P$ "" , . $P$- , , , . 倔 (. 2.3.4.5--10), : " $(1-S)\bmod(P-1)$ 0, $P$ \emph{} , ". , . 100000, 9- , 18 , 5.4.6F . 9- 60 $1{29\over30}$ , . . " " , , 7.4 . ゅ $P$, , , , . %%435 \section . , "" , . , , . . ㌅ $P$ . , ; , $P$. , , , . , . . (., , .~2). , , - ; , , !   , , "" , . , (. . ), ; , . , , .~92; , ' , . , . , (1) $n$ $72.5+0.005n$~; (2) 100000 ; (3) $0.004$~ ; (4) \emph{ } , ; (5) , , , . . $P$- , %% 436 $P+1$ : $P$--- 1--- ; $B=100000/(P+1)$ . , $L$ ; $L/B$ ; , ( ) $$ 2\left(72.5{L\over B}+0.005L\right)+0.004L=(0.00145P+0.011545)L. \eqno(2) $$ , $P$- $L$ $(\alpha P+\beta)L$ , $\alpha$ ~$\beta$--- , , , . 풀 \picture{. 92. 16 ...} . , , .~92 , . ( "") $L_0$.. ⎃ 9 ~10 $(2\alpha+\beta)(2L_0)$ , 11 $(3\alpha+\beta)(4L_0)$ 12 $(4\alpha+\beta)(8L_0)$ . , , $(52\alpha + 16\beta)L_0$ . "16" : . "52" $\alpha$ , \dfn{ }; , , , . , .~92 $(2+4)+(2+4)+(3+4)+(2+3+4)+(2+3+4)+(3+4)+(4)+(4)=52$. $\cJ$--- , $D(\cJ)$, $E(\cJ)$ . : %% 437 \proclaim ⅎ H. , $P$- $L$ , $(\alpha P+\beta)L$ $S$ , $\cJ$, $\alpha D (\cJ)+\beta E(\cJ)$ $S$ . \noindent (풀 , . 倁 ACM 1963 .) $\alpha$ $\beta$--- ; , \dfn{}, $\alpha D(\cJ)+\beta E (\cJ)$ $\cJ$ . , \emph{ }. $n$ , , $n$ . \proclaim ⅎ K. $A_m(n)$ $1\le m\le n$ $$ \eqalignno{ A_1(1)&=0; & (3) \cr A_m(n)&=\min_{1\le k\le n/m} (A_1(k)+A_{m-1}(n-k) \rem{ $2\le m\le n$;} & (4) \cr A_1(n)&=\min_{2\le m\le n} ((\alpha mn+\beta n+A_m(n)) \rem{ $n\ge 2$.} & (5)\cr } $$ ⎃ $A_1(n)$ $\alpha D (\cJ) +\beta E(\cJ)$ $\cJ$ $n$ . \proof (4) , $A_m(n)$ $A_1(n_1)+\cdots+A_1(n_m)$ $n_1$, \dots, $n_m$, , $n_1+\cdots+n_m=n$. ␅ ~$n$. \proofend (3), (4), (5) . $k_m(n)$---, $A_m()$. ⎃ $n$ , $m=k_1(n)$ ; $k_m(n)$, $k_{m-1}(n-k_m(n))$, $k_{m-2}(n-k_m(n)-k_{m-1}(n-k_m(n)))$, \dots . 풀 $\alpha=\beta=1$ .~1. ; "4:9:9" $n=22$, , , $\cJ_22$ 22 $\cJ_4$, $\cJ_9$ ~$\cJ_9$ (.~93). ; , 5:8:9 , 4:9:9. %% 438 \bye