备战2023年重庆数学中考二轮复习知识点13数论（阅读理解）（解析版）.pdf

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1.
A A=MXN,MN!M"N#
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Q(A)
W
VA=1472=23X64^“.”.P(A)=(2-3)+(6+4)=9,
Q(A)=(2+3)-(6-4)=3,.F(A)=9=3.
Q(A)3
(1)Z[1951736]“.”?_`abI
(2)OA“.”!c(A)d5efSghijklm#A.
nop (1)1736“.”195N“.”b
4
V1736=31X56,3+5=8,1+6=7,
...1736“.”
7195=13X15,1+1W8,
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#)$"$#"N#)$"#RSRT&t(4),
.P(A)=a-b+\5-a-b=l5-2h,Q(A)=a+b-(S-a-7+h)=2a-1,
,F(A)=F'(A)!c(A)d5ef
Q(A)
wc(A)=P(A)=15-2b=,*.TWa<8,0WbW7,
Q(A)2a-l
lW2a-1V15,1W15-28W15,:.
€2=1,
15~2b=5,ƒ
2a-l
[2a-l=l…[2a-l=3
I15-2b=5-115-2b=15
‡:ˆ=1…‰a=2,
€ˆ=1
lb=5
M=15,N=72,
=MXN=1080,
€[a=2
lb=O
M=20,N=67,
=MXN=1340,
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Ž€k=3
15-2b=]5)ƒ
2a-l
pa-l=l,
115-2b=15,
‡ ˆ=1,
lb=O
‘M=10,N=77,
A=MXN=770,
’2A#“”&1080…1340…770.
2.)$•–$—5#˜™eM,š2#$›Nœ!N&
ž.QŸ$ #¡T&mi,¢$ #¡T&m2,TF(M)=
£¤¥,Oc(M)&e,M&“¦§¨©”.
5
>
M=1276,7-2=5,ª”=12,ª?2=76,F(M)=22«1Z=20&eA1276
5
¦§¨©IM=2493,9-4=5,"i=24,ª?2=93,F(M)=2¯24+91&=141N&
55
e¦§¨©.(1)Z[3168,4387]&¦§¨©_`ab.
(2)S“¦§¨©”±²!š$%d5efSjkl
m#hiS#”.:.
nop (1)M=3168,6-1=5,ª“=31,ª?2=68,
F(M)=2Xm1+6X=26&e
5
..3168“¦§¨©”I
M=4387,8-3=5,mi=43,³2=87,
F(M)=2X43+87=221=e,
55
...4387N“¦§¨©”I
(2)r˜S&abed(1W“W9,1WCW9,lWdW9,!›Nœ)
IS“¦§¨©”
Ac-b=5,
..c=A+5,
:.a+h+c+d=a+h+h+5+d=a+2h+d+5,
KW9,
lWb+5W9,
0W4,
q´µ¶9,l·dW9,
9Wª+2&+d+5W31,
¸¹b,dšNœ,
J12Wª+2ª+d+5W29,
VS#š$%d5ef
:.a+2b+d+5=15…20…25,
ª+28+4=10…15…20,
IS“¦§¨©”.F(M)=2(10a+b)+10c+d=20a+2b+10(b+5)+d
55
=2°a+12b+d+5°=4a+26+2b+de,
55
..2³V5#º,
.2b+d=5…10,
²,:.
q"²,
.2h+d=5,
.4=5,
lWbW4,
.,.b=\,d=3…6=2,d=\,
.,.a=5,b=1,c=6,d=3…a=5,b=2,c=7,d=\,
ƒjklm#hiS#”&5163…5271.
3.
»¼½¾¿™en,
n#š2#$ÀNœÁ!N&žÂ
Ã,Ä&“Å6”Q“Å6”#¿2#$ÆÇÈÉÊˇÌ
5NÁ#¡“Å6”8Ä6Å6#"111#ÍT&M(ª).>
“=123,
ÊˇÌ132Î213Î231Î312Î321Ä5¡#“Å6”Ä6“Å6”#&
123+132+213+231+312+321=1332,Ï&1332t111=12,hË“(123)=12.
(1)ÐÑ M(125)M(361)#”
(2)rs/“Å6”42Ós#)2#$25
Ót#–2#$!t#)2#$•s#–2#$¹2IÔÕ
kÖ×.O13M(s)+14>(/)=458,+Ø#”ÙÚÛ
ˆM(t)
nop (1)M(125)=(521+512+215+251+125+152)+111=16,
M(361)=(316+361+136+163+613+631)4-111=20I
(2)f“Å6"a=100x+42,b=205+10y,
.M(s)=(200x+42+24+20x+402+204+2x+420+240)+lll=2x+12,
M(/)=(205+10)+502+lQy+250+x+520+y+100)+25+100y+52)-Mll=2y+14.
V13M(s)+14M(r)=458,
A13(2x+12)+14(2y+14)=26x+28y+352=458,Ü13x+14y=53,
W,.,x=y+2,
.(13x+14y=53
Ix=y+2
‡(x=3,
Iy=l
M(s)=2X3+12=9
*'k=M(t)2X1+148":.
4.»¼¨#
š2#$ݼ–2#$»,Þß+,Ä
&“àá”.
12321,24542I»¼“àá”OsâÌãœä
2#$%R#廔œÁ+,Ä“àá”&“æçàá”

12321,25852,35753O“æçàá”xsâÌã²2#$%T&
è2#$%T&N,Tc(x)=2M+N.
x=12321,+1+3+1=5,
N=2+2=4,hËF(x)=10+4=14.
(1)éêëZ[15951]&“æçàá”OéSgF(15951),ON
é`abI
(2)ìíx“æçàá”!xd7ef¸c(î)fË5ïI,Sghij
klm#¨“æçàá”x#”.
nop (1)15951&“æçàá”,
1+9+1=11,N=5+5=10,
.F(15951)=2M+N=32.
(2)bx“æçàá”rx#2#&0,)2#&4–2#&c,
+ð2#6ñ2#a,
.=2a+c,N=2b,
!-b\=\b-c\,
.,.F(x)4a+2c+2b,!a=c…“+c=2b,
d7ef
qlOOOla+lOlOb+lOOc
=1429t+144/2+14c+~2a+2b+2c)
7
:.-a+b+cd7ef
€a=c-a+b+c=b,!6&e
.2=0…7,
VF(x)fË5ï1,
qF(x)~1ô6a+2bl_z,4_a+2b-l
555
.a+2b-ld5ef
!“&e
.'.b=0,a=6…1I…L=7,a=2…7I:.
/.x=60606…27272…77777…10101
‹€a+c2b-a+h+c=2c-b,
!c&e
Ü-9W2c-6W18,
.2c-b=-7…0…7…14,
VF‰%÷fË5ï1,
qF‰x÷-l=10b-2c-l=26_2c+l
"~555
A2c+1d5ef
I1W2C+1W19,
/.2c+l=5…10…15,
.c=1…6,
.".c2,b=4…c=7,b=7…0‰ùú÷
…77777,
’2Êíx#”&60606…27272…77777…10101…64246.
5.»½¾˜ªQĘªð2$")2$»ûΖ2$"
2$»û¢ÊˇÌ¡#˜üTc‰ª÷=ÜÜ6.>
“=1423,»ûð
99
2$")2$ý–2$"2$‡Ì2314,hËF‰ª÷=1423-2314
99
=-9.
˜”jkð$"–$#¼)$"$#+,
Ä“þÿ”1423, 1+4=2+3,1423.
18062,!"#$%&'()*+, -.2
/“”N23(456(422781,9:“”;<=>3
?11-@ABN2DEF.
GHIJH1F8062=8062-6280=18.
88
!"MNOP'(Q=1000a+100b+10c+d,VWb,c,d 0-92-.
$p)=1000a+100b+10c+d-1000c+100d+10a+b=990a+99b-990c-99d=
9999Y
\Oa+b-10c-d,
,.Z,b,C,d -#$%&'(FH*-.
2PN=mnpq,:.
abcde))=p+g,
aN23(456(422781,e)=2)-1,
N=1000"?+100)+1Op+q
=100bzz+10U+9p
=1001m+119)-9.
d>11-@
A1001m+119n-9=91m+10)+9n-9,
1111
..g5h -.
11
i9) -
*.n=1,
p--2)-1=1,
AAf=1001m+110.
;>3-@
...1001m+110333^+36+2m+2,
=
33
...k2 -.
3
il1
.*.772=2m5m8,
N=2U2m5115m8118.
VF(2112)=9,F(5115)=36,F(8118)=63,.F(TV)2DEF9.
6.nop";rHsp2+g,VW)tq*u(ptq2(4v<3
(4w? 10,xyM “z{”|M=fT+q2MNy “z{r
H”236=12?+92,12t922(4v<3(4w?}$10,236
“z{”.
(1)~212€“z{”.‚"ƒa.
(2)|'(“z{”M„…“z{rH"†M=p2+q,‡pˆ‰q2Š‹Œ
s2'(N,/N;>7-@9N2Ž(4w?;>3-@A
+‘’“2M.
GHIJH:(1)212=112+91,:.
.g•2“z{”.
(2)Pp23()?()
xq23(10-m,(n,
2Ž(4w?m+n+W-)?+)=10+2%
;>3-@
'.n=1m"=4mn=7,
›”=1=1000/n+100+100-10/n+1=990w+201,
;>7-@
.*.A/=312+71=1032.
›)=4=1000/W+400+100-10/n+4=990w+504,
;>7-@
7+34=5510.
›)=7=N=T000/n+700+100-10/n+7=990m+807,
;>7-@
472+67=2276.
¡¢£‘’“2M+1032?5510?2276.
7.#$%&'(opA,nA‘Ž(¢24¥¦v<9A23(45
§(4¨1,(456(4¨1,xy:'(opA “©”.#$
“©"A=abcd()ªb,c,d-91,0W«c,dW9),¬2§(
4?6(4Œs2u( 3(4?(4Œs2u( ®‡:u
u(A?¯°f.¬2§(4?3(4Œs2u( ®¬26(4?(
4Œs2u( ²‡:uu(A?¯°s,´bF(A)=µ.
9
4=1324, 2-1=1,4-3=1,¶A“©”=13+24=37,S
=12+34=46,xF(A)=·~~46=_L
9
(1)»¼'(2637,4758½ “©”AF(2637),F(4758)2F.
(2)/'(Pªµ½ “©”P26(4 4,F(P)W0,µ2§(4 :.
2m,VW9,” ¿-(4 n7,VW2W)W109” ¿-›
E4a;>3-@=A+‘’“2'(Q.
FQ
GHIJH1aÂ&deF2637=26+37-23+67=7.
9
F4758=4"58-45+7Ã.=-2.
9
2;g'(P,Q½ “©“P26(4 4,Q2§(4 2{(
4 n-
2(4 5,µ23(4 2Å+1,µ26(4 2,
PP=1000x+400+10(x+1)+5,µ=2000Ç+100(n-2)+10(2w+l)+n~\,
$F(P)=10x+4+10(x+1)+5-10x-x-l~~45=9x-27=.É_j
Ë9-9
F(°)=20in+n-2+(2m+l)+n-l-20m-2irr1-10(n-2)-n+l=2”
9
.F(P)-x-3
F(Q)2m-n+3
Ï1Ã_;>3-***@9P(P)WO,1WXW9,
F(Q)
...x-3=3mx-3=6,Hex=6mx=9(ÑÒÓ=P23(410),
F(P)=3-,
F(Q)2m-n+3
2m-n+3=-1m2)?-n+3=1,
ԛ2m-)+3=-1=)=2w+4,,.%W3,
l2<2m+4<10
›m=\=)=6,x0=2435.
›m=2=)=8,xQ=4758.
›m=3=n=10,xµ=6879.
֛2m-)+3=1=n=2in+2,
l2<2m+2<10
1WmW4,
›)2=1=)=4,xµ=2233ÑÒ.
›m=2=)=6,xµ=4455ÑÒ.
›Å=3=)=8,xµ=6677ÑÒ.
›)7=4=n=10,xµ=8899ÑÒ.:.
¡¢µ=2435m4758m6879.
8.×Ø1#$'(opM,nM‘Ž(¢24½¦ 0,¬26(¢2
45§(¢24¨1,(¢2453(¢24¨1,xyM “ÙÚ
”.#$“ÙÚ”M,<=‡M2(4ÛÜÝ3(ª3(4ÛÜÝ6
(ª6(4ÛÜÝ(eݍ2'(MyN “Þß”´bB(M)
=àà¼=2378, 3-2=1,8-7=1.2378"ÙÚ”.‡M2
9
(48ÛÜÝ3(‡3(47ÛÜÝ6(‡6(43ÛÜÝ(eÝ“Þ
ß"N=2783,F(2378)=2378,78375.
×Ø2#$%&'(opabcd=1000"+100b+10c+d(µªb,cªd-9IWaW
9,
OWb,c,4W9),´bG(abed)=cxd-axb.
áâ¢×ØgHãOäåÂ
(1)~2367ª7934¦“ÙÚ”‚"ƒa.nA#æ2F(M)
2F.
(2)!"#$%&“ÙÚ”M,F(M)* -
(3)»¼PªQ“ÙÚ”VWB2§(4 Å(Å-91W/MW7),3(
4 (4 5,3(4 s(s-93WsW8),9/G(P)
+G(Q);>13-@AB(Q)(1)H3-2=1,7-6=1,
2367“ÙÚ”.
M=2367,N=2673.
.F(M)=2367-2673="34
9
9-7=2,4-3=1.
.27934¦“ÙÚ”.
(2)!"P“ÙÚ"M=x(x+1)y(y+l)=1000x+I00(x+1)+10y+y+l=
1100x+lly+101.
7V=1000x+100y+10(y+1)+x+l=1001x+110)H-lI.
N=99x-99y+99.
.F(M)=tH=llx-lly+:.
y*-,
ggg#$%&“ÙÚ”M,F(M)* -.
(3)HaÂ&eP=1000/n+100(/M+1)+80+9=1100*+189.
2=4500+105+5+1=4501+115.
.G(P)=8X9-m({+1)=-nr-m+12.
G(µ)=s(A+1)-4X5=?+5-20.
.G(P)+G(Q)=?-m2+s-m+52
=(s-Å)(s+/n+l)+52.
,3WsW8,s>)7,G(P)+G(Q);713-@
.s+m+\1327
)?=5ms=8,m=4.
.*.(2=4501+11X7=4578m0=4500+11X8=4589.
›(2=4578=ªF(µ)=4578-4785=_23.
9
›(2=4589=F(Q)=4589-4895=_34,
9
9.×Ø1/¿-2Ž(¢24w?;>3-@x:è;>3-***@.
éwhsê.
×Ø2u()??ë()¬ìŽ(¢24*¦ 0,‡m%&(¢
24° 2u(23(4‡n%&(¢24° í2u(
2(4îï:ðzñò2+2u(2?¯ B(m,"),B(12,
345)=13+14+15+23+24+25=(11,369)=13+16+19+13+16+19=96.
(1)óôF(16,123)=222,A!›);>3-@=FCm,))b;
>6-***@.
(2)/u(s=21x+y,ë(f=121x+y+199(VW1WXW4,1WõW5,9
xªy½ -)ÛÜë(r26(4?(4eݍf',›/ts2(
42372?;>11-@=y:ö2us?f “÷ø#”A+“÷ø
#"WF(s,t)2D¨F.
GHIJH(1)F(16,123)=11+12+13+61+62+63=222,
¶Iù 222,
!"m=xy,n=abc>:.
aÂ&ea+b+c?abc*;>3-@
.".F(m,n)=10x+a+10x+)+10x+c+10y+a+10y+Z>+lQy+c,
=30x+30y+2a+2b+2c,
=5X6(x+y)+2Ca+b+c),
aÂ&ea+b+c?ü*;>3-@
.gg›”;>3-@=,FCm,n)b;>6-@;
(2)s=21x+y,f=121x+)+199(VW1WXW4,lWyW5,9xªy½ -)
gJ+3(x+y)=100Cx+y-1)+10(2x)+x+2+3(x+y)=124x+103y-98
."+3(x+y);>11-@
t'+3(x~ny)Jlx+ggy-gUx+dy+l=Hv+9y_Q+3x+4y+l
~ii=iln~~
.3x+4y+l
-
11
.'1WXW4,lWyW5,
..8W3x+4y+lW33
›3x+4y+l=11
'.x=2,y=l
,.s=43,f=442›3x+4y+l=22..x=3,y=3
,.s=66,f=565
›3x+4y+l=33
.,.x=4,y=5
.,..y=89,r=688
.F(s,t)D¨F=F(89,688)=86+88+88+96+98+98=554
10.#$ë(m,/VŽ(¢24*¦ 09¥¦v}.xy:ö2
“…¼”.‡“…¼”m
%&u(¢24ÿ

6.6
(m).
D(235)=23+25+35+32+52+53=220.
(1)%&'D(123)132(
(2))*:D(,?)./2201;:.
(3)FCm)=D145(235)=D.(23§)=22Q=“89",;<
222222
=>?@=>3ABF(,)17D1,F)GH;9”nL.
MNOPN'(1)QRST9'
D(123)=12+21+13+31+23+32=132,
UOV'132.
(2)W89m=100a+108+c,
.D(in')10a+b+10a+c+10b+c+10b+a+10c+[+1Oc+b
22a+22b+22c22(a+b+c),
UCm)./2201(
(3)W89n100x+10y+3x,
(.m)22(a+b+c),
F("?))=a+6+c,
22
D(,)=22(x+y+3x)
=22(4x+y)
.'.F([)=4x+y,1W3XW9,
(.1WXW3,lWyW9,
(.5W4x+yW21,
,:F(n)17D1,
4x+y=8de15,
'lWxW3,
(.x=lf2d3,4x+y=8de15,yg0Bx,y,3xhijk
lx=l,y=4m89143,
lx=2,y=7m89276,
GH;opqN,6;t>uvw@>ux0,y
“z{”|}~s>t>€G(N).
‚ƒP(s,f)=G(s')'m+G(r)(s,fz{"ˆ‰Š)B5(523,
413)=9,P(312,633)=-:.
:945,V4+5-9=0,945?“z{”G(945)=4X5=20.
634,73+4-6=1^0,6634i?“z{”.
(1)FŽ'817?“z{”,527i?“z{”(Ž“?”d“i
?")(
(2))Šj”L(
(3)9s?>i1“z{”~s>a,>b,s
>‘’ss>‘’@@>‘’
“”6st
s'x./1701)GH;MNOPN'(1)›817œ
V1+7-8=0,
817?z{;
›527œ,
V2+7-5W0,
27i?z{.
UOV'?i?(
(2)VP(523,413)=9,QRs>t>€G(N),
G(523)=2X3=6,G(413)1X3=3,
ž
6,?+3,=9Ÿ.
:P(312,633)=-5,
QRs>t>€G(N),
G(312)=1X2=2,G(633)=3X3=9,
ž
2m+9n=-5
¡¢Ÿ N *=2,”=-1.
(3)—z{‚ƒ
9s=100(a+b)+\0a+b,
—z{‚ƒ–9IJ
9s'=100a+10/?+(a+b),
ts'x./1701
100Ca+b)+\0a+b-[100a+10Z?+Ca+b)]./1701
ž100[+100ft+10a+Z?-1004-106-4-6,
ª« s-s'=9(1Ob+a),
/.lOb+a17A:.
Tsz{B+6W9,¬1,
'MV9,1:.lOb+a®100,
¯°100±17A²:
17,34,51,68,85
610³+,=17,a=7,b=l,i´™ST,
6106+4=34,a=4,b=3,´™ST,
6106+=51,a=Lb=5,´™ST,
610³+=68,,=8,b=6,a+b>9fi´™ST,
10Z?+,=85,,=5,b=8,a+h>9,i´™ST,
µ=
$=743d5=615,
¶UP(743,615)=G(743)m+G(615),=4X3X2+1X5X(-1)=15.
12.·¸.'¹®ºpq;t@>uk®>t»>
u2Ay“A”.6¼‚5(N)»>3At>
xQ(N)»>t>u:F(N)=P(N)
Q(N)
'3621,V6+2=2X(1+3),¾3621?“A”F(3621)=3;o¾1=2.
3+1
¿À4271,(2+7#2*(1+4),¾4271i?“A”.
(1)ÁÂ3531,4682?Ã?“A”|ÄÅƗ(Ç?F%&5(N)L(
(2)6ºpq?“A”~s>./501B>t@>
./301F(n)0)´™IJ”.
MNOPN'(1)V(5+3)?(1+3)2A
./.3531?A
V(6+8)i?(4+2)2A,
./.4682i?A
F(3531)="=2.
3+1
(2)Wpq”»f@fsfÈÉ?4fb,c,d,
.”?As./501t@./301F(,)0
.,.h+c=2(a+d),c=0d5,6+d=0d3d6d9,ÊËÌ0
a+