64æã®ãã©ã³ãïŒåçš®ããŒã¯ã®14,15,16ãäœã远å ããŠãèš64æã«ããããã¯)
ãããèŠåã§é
åããããã®ãæºåããã
(1)芳客ã«å¥œããªåæ°ã ããã®ããã¯ãã«ãã(ä»»æã®å Žæã§äžäžã®ãã±ãããå
¥ãæ¿ããã)
ãããã
(2)ãã®åŸäžãã6æã®ã«ãŒãã衚åãã«ããŒãã«ã«äžŠã¹ãããã
ã(ãã®ææŒè
ã¯äžŠã¹ãŠããã«ãŒãã¯èŠãªãããšã«ããã)
(3)䞊ã³çµãããããã®ã«ãŒãã®è²ãèµ€ãé»ãã®ç¶æ
ã䞊ã¹ãé çªã§èšã£ãŠãããã
(4)ãããèããŠæŒè
ã¯äžŠãã 6æã®ã«ãŒãã®åå(ããŒã¯ãšæ°å)ãå
šéšèšãåœãŠãã
[åç]
è²ã®æ
å ±ãã0,1ãããªã6ãããã®å(abcdef)ãåŸãããã
abã®é
åããæåã«äžŠã¹ãã«ãŒãã®ããŒã¯(4çš®é¡å¯Ÿå¿ã§ãã)
cdefã®é
åãããã®ã«ãŒãã®æ°å(2鲿°è¡šç€ºãšã¿ãŠ16éãã®éããäœãã)
ãšãããããåãã«äžŠã¹ãã«ãŒããšãªãããã«å¯Ÿå¿ãããŠããã
次ã«2çªç®ã«äžŠã¹ãã«ãŒãã¯
ä»äžŠãã§ãã1çªç®ã®ã«ãŒããåãå»ãããã¯ã®ããã ãžçŽããã
次ã«åºãã«ãŒãã®è²ã§6åã®ãããåãäœã£ãå Žåã
ããã2çªç®ã®ã«ãŒããšå¯Ÿå¿ããããã«ã以äžé
åç¶æ
ã
次ã
ãšèµ·ãããé çªã«ã«ãŒããçµã¿åããããã°ãã«ãŒãã®é
åç¶æ
ãã
6æã®ã«ãŒãã®ãã¹ãŠã®ååãåœãŠãããšãå¯èœã«ãªãã
åŸã£ãŠåãã«äžŠã¹ã6åã®ãããç¶æ
ãããæ¬¡ã«åºãã«ãŒãã®è²ãã©ã決å®
ãããã®ã«ãŒã«ãèŠã€ãåºãããšããã§ããŠããã°èªåçã«ã«ãŒãã®æ°åã
決ããããããšã«ãªããç®çã®çŸè±¡ãå¯èœãšãªã64æã®ãã©ã³ãã®é
åã
èŠã€ããããšã«ãªãã
ãããå
ã«ãã®é
åã®ã«ãŒã«ãæ±ããŠã³ã³ãã¥ãŒã¿ã§è©Šè¡é¯èª€ãç¹°ãè¿ã
å®éšããŠããŠå¶ç¶ãéãªããã®é
åãäžå¿èŠã€ããŸããã
äœãã«ãããããç¶æ
ãèŠã€ããããã¯ã®åæã®é
åç¶æ
ã«æ»ã£ãŠããŸã£ã
ãã®ãšãããã ã«ãã£ãã«ãŒããã«ããã®çµæãããã«ãã2ã€ã®å Žåã§ã¯
åºæ¥ãªããªããŸããïŒãã®ç¶æ
ãèµ·ããããšã¯ãŸããªããšã¯æããŸãã)
ãããå·ãšèšãã°ä»ã®ãšããå·ã§ãã
éåžžã®52æã®ãã©ã³ãã§ããã詊ã¿ãŠããã®ã§ãããããã64æã§ã®æ¹ã
ããæãæããã®ã§æ¢ããŠãã®ç¹æ®ãã©ã³ãã§ææŠããŸããã
èå³ãåºãæ¹ã¯ãã®é
åç¶æ
ãèŠã€ãåºããŠäžããã
ãã£ãšå¹çããæ¹æ³ããç¥ãã®æ¹ã¯æããŠäžããã
NEWNo.1427GAI仿¥ 06:46
ãã°ãã°è©±é¡ã«äžãã de Bruijn æ°åã® B(2,6) ã§ããïŒ
NEWNo.1428DD++仿¥ 08:09
ãã¶ãçµæçã«åãé¢ä¿ããŠãããšæããŸãã
NEWNo.1429GAI仿¥ 08:27
次ã®9åã®ã°ã©ããåæã«æããŠã¿ããã
C1:x^2+y^2=9^2
C2:(x-15)^2+y^2=6^2
C3:(x-6)^2+y^2=15^2
C4:(x-189/19)^2+(y-180/19)^2=(90/19)^2
C5:(x-81/31)^2+(y-360/31)^2=(90/31)^2
C6:(x+33/17)^2+(y-180/17)^2=(30/17)^2
C7:(x+351/79)^2+(y-720/79)^2=(90/79)^2
C8:(x+135/23)^2+(y-180/23)^2=(18/23)^2
C9:(x+357/53)^2+(y-360/53)^2=(30/53)^2
ãªã
ããã«ç¶ã3åã®åã®æ¹çšåŒã¯ïŒ
No.1421GAI9æ16æ¥ 04:47
äžè¬åŒã¯
(x+9(4n^2-25)/(4n^2+15))^2+(y-180n/(4n^2+15))^2=(90/(4n^2+15))^2
ãªã®ã§ãç¶ãã¯
(x+1539/211)^2+(y-1260/211)^2=(90/211)^2
(x+2079/271)^2+(y-1440/271)^2=(90/271)^2
(x+897/113)^2+(y-540/113)^2=(90/339)^2
(x+675/83)^2+(y-360/83)^2=(90/415)^2
(x+4131/499)^2+(y-1980/499)^2=(90/499)^2
(x+1653/197)^2+(y-720/197)^2=(90/591)^2
(x+5859/691)^2+(y-2340/691)^2=(90/691)^2
(x+6831/799)^2+(y-2520/799)^2=(90/799)^2
(x+525/61)^2+(y-180/61)^2=(90/915)^2
(x+8991/1039)^2+(y-2880/1039)^2=(90/1039)^2
(x+10179/1171)^2+(y-3060/1171)^2=(90/1171)^2
(x+3813/437)^2+(y-1080/437)^2=(90/1311)^2
ã»ã»ã»
ã®ããã«ãªããŸããã
No.1422ãããã9æ16æ¥ 08:01
äžè¬ã®å Žåã«ã€ããŠèããŠã¿ãŸããã
ãŸãä»åã®èšå®ã¯æåã®2åãå³ã«9ç§»åããŠ
äžå¿(15,0)ååŸ15ã®å((x-15)^2+y^2=15^2 â x^2-30x+y^2=0) ãš
äžå¿(9,0)ååŸ9ã®å((x-9)^2+y^2=9^2 â x^2-18x+y^2=0) ã«ãããšãäžè¬åŒã¯
((4n^2+15)x-360)^2+((4n^2+15)y-180n)^2=90^2
ãšãã綺éºãªåœ¢ã«ãªããŸãã
ãããŠããã«ååŸãäžè¬åãããš
åç¹ã§æ¥ãã2å
äžå¿(a,0)ååŸaã®å(x^2-2ax+y^2=0)
äžå¿(b,0)ååŸbã®å(x^2-2bx+y^2=0)
ã«æãŸããåã¯
((((a-b)n)^2+ab)x-ab(a+b))^2+((((a-b)n)^2+ab)y-2ab(a-b)n)^2=(ab(a-b))^2
n=0ãæå€§åãn=±1ãæå€§åã®é£ãn=±2ããã®é£ãã»ã»ã»
ã®ããã«ãªããŸããã
aãšbã®å€§å°é¢ä¿ã¯ã©ã¡ãã§ãOKã§ãããè² ã§ãOKã§ãã
aãbãè² ãªãã°xïŒ0ã®ç¯å²ã§åãããšãèµ·ããã
aãšbã®ç¬Šå·ãç°ãªãå Žå(æåã®2åãåç¹ã§å€æ¥ããå Žå)ã¯å€æ¥åã§åæ§ã®ããšãèµ·ãããŸãã
ïŒã€ãŸãn=0ã®ãšã2åãå
ãåãn=±1ã®ãšããã®åãšå
ã®2åã«æ¥ãã倿¥åãã»ã»ã»ïŒ
No.1423ãããã9æ16æ¥ 19:19
äžè¬åãããåŒã§æ©éå®éšããŠã¿ãŸããã
a=-9,b=6
ã§ïŒåãæã
n=0ã§å€§åã
n=1ã§ïŒã€ã®åã«æ¥ããåãäœããŠããã®ã§ãã
n=2,3,4,ã§ã¯äžæ¹ã«åãã£ãŠåãé£ãªã£ãŠããè¡ãã®ã§ãã
ãããa=-9ã®åãšå€§åã«æ¥ããæ§ã«å·Šã«é²è¡ãããããªãã®ïŒçµµæçã«ãã¡ãããã£ãããã®ã§ïœ¥ïœ¥ïœ¥)
ã«ããã®ã¯ã©ããããããã®ã§ããããïŒ
No.1424GAI9æ17æ¥ 07:06
a=15,b=9ãšãããšãã®å³ãå·Šã«18ç§»åãããã®ã§ãããã
((((a-b)n)^2+ab)x-ab(a+b))^2+((((a-b)n)^2+ab)y-2ab(a-b)n)^2=(ab(a-b))^2
ã®xã(x+18)ã«ããŠ
a=15,b=9ãšããã°ããã§ããã
ãŸãxã(x-12)ã«ããŠa=-15,b=-6ã«ããã°å察åŽã®åãæããŸãã
äžè¬åœ¢ã®åŒããããšãããªå³ãç°¡åã«æããŸããããªãã£ãã倧å€ã§ããã
No.1425ãããã9æ17æ¥ 10:56
ãŸãxã(x-12)ã«ããŠa=-15,b=-6ã«ããã°å察åŽã®åãæããŸãã
ãããŒïŒ
ãã®ã¢ã€ãã¢ã¯æã£ãŠãããŸããã§ããã
äžè¬åããããšã§å¿çšã®éãåºãããŸããïœ
No.1426GAI9æ18æ¥ 06:22
t=â2
ã§ããæ
(1)P=1/(t^2+3*t+1)
(2)Q=1/(t^3+3*t+1)
ãªãåŒãæçåããããã
ããŠããããã©ã®æ§ãªåŒã«ã§ãããïŒ
No.1417GAI9æ15æ¥ 15:38
(1) (t^2+3*t+1)*(8*t^2ïŒtïŒ5)ïŒ41ããªã®ã§ãïŒ(8*t^2ïŒtïŒ5)/41
(2) t^3+3*t+1=3*t+3ããªã®ã§ã (3*t+3)*(t^2ïŒtïŒ1)ïŒ9ããããQ=(t^2ïŒtïŒ1)/9ãã§ããïŒ
No.1418管çè
9æ15æ¥ 16:17 ãã£ããªã解決ããã¡ãããŸããã
No.1420GAI9æ15æ¥ 20:58
(1)x^2+y^2+sin(7*x)+sin(7*y)-1=0
(2)x^2+y^2+sin(7*x)+cos(7*y)-1=0
(3)x^2+y^2+cos(7*x)+cos(7*y)-1=0
(4)|x|+|y|+sin(|7*x|)+sin(|7*y|)-1=0
(5)|x|+|y|+sin(|7*x|)+cos(|7*y|)-1=0
(6)|x|*|y|+sin(|7*x|)*cos(|7*y|)-1=0
ã®ã°ã©ããåçã«å€åããæ§åããæ¥œãã¿ãã ããã
No.1415GAI9æ9æ¥ 08:32
Grapesã§æç»ããŸããããã®ã°ã©ãã¯ææ¥ä»ã§ã¢ããäºå®ã§ãã
No.1416管çè
9æ9æ¥ 18:22 ïŒÃïŒã®ãã¹ç®ãäœã
客ã«ïŒã€ã®æ ã«å¥œããªäžæ¡ã®æ°åãåæã«åããŠãããã
0ãå«ãã§ãè¯ãããæ°åãéãªã£ãŠããŠãæ§ããªãã
次ã«åããè¡åã®åè¡ã®3ã€ããæ°åããããããåæã«ãããã
1åãã€éžãã§ããïŒæ¡ã®æŽæ°(第1è¡ãçŸäœã第2è¡ãåäœã第3è¡ãäžäœ)
ãäœã£ãŠãããã
åãããã«ïŒã€ç®ã®ïŒæ¡ã®æŽæ°ãåè¡ã§äžã§éžãã æ°ã¯é€ãæ®ã2ã€ããéžã¶ããšã§
äœã£ãŠãããã
ãããŠãåè¡æ®ã£ãæ°åãã3ã€ç®ã®æŽæ°ãäœãã
ããããŠå®¢ãä»»æã«äœã£ã3ã€ã®ïŒæ¡ã®æ°ã®åèšãããŠãããã
(0ãå
é ã«æ¥ãå Žåã¯ïŒæ¡ã®ãã®ãšãªããïŒ
å¿è«ããªãã¯å®¢ãäœã£ãïŒã€ã®æ°ã¯èŠãªããã®ãšããã
ããªãã¯å®¢ãèšç®ã§æ±ããã§ãããåèšã®æ°ãäºèšãšç§°ããŠçŽã«æžãã€ããã
客ãåèšæ°ãçºè¡šããããŠããªãã¯ãã®äºèšã®çŽãèŠããã
ïŒããŠãã®ããã©ãŒãã³ã¹ãæåãããããã«ã¯ãã©ããªæ¹æ³ã䜿ãã°å¯èœã§ããããïŒ
No.1412GAI9æ2æ¥ 12:52
çãã¯ç®¡ç人ãããæžããŠãããŠããšããŠã1ã€ããã³ãã©ãããã
客ã3ã€ã®æ°ãäœãåã«ãããªããšãäºèšãã«ãªããªãã®ã§ã¯ã
No.1413DD++9æ3æ¥ 14:15
確ãã«9ãã¹ç®ã®æ°ã
5 1 3
3 6 9
4 2 8
ãªã客ãèšç®ã§åºãæ°ã¯
(5+1+3)*100+(3+6+9)*10+(4+2+8)
ãªã®ã§ãããã¯äžã®è¡åã90°巊å転ãã
3 9 8
1 6 2
5 3 4
ãšçºããŠããããèšç®ããšãã°ããããšã«ãªããŸãã
DD++ããã®ããã³ãããããŸãããã客ãäœãæ°ãèŠãŠããªãã®ã ããäºèšãšã¯è¡ããªããŠã
äºç¥ããã©ãŒãã³ã¹ãšã¯ãªããã§ã¯ãªãããªïŒ
No.1414GAI9æ5æ¥ 07:01
A^2+B^2
ã¯å æ°åè§£ããããšã¯åºæ¥ãŸããã
A=X^2,B=2*Y^2ãšçœ®ãçŽããš
X^4+4*Y^4
=X^4+4*X^2*Y^2+4*Y^4-4*X^2*Y^2
=(X^2+2*Y^2)^2-(2*X*Y)^2
=(X^2-2*X*Y+2*Y^2)*(X^2+2*X*Y+2*Y^2)
ãšïŒã€ã®ç©ã§äœãçŽããã
åãã
A^3+B^3=(A+B)*(A^2-A*B+B^2)
ãŸã§ã¯åºæ¥ãã
A=X^2,B=3*Y^2ãšçœ®ãçŽããš
X^6+27*Y^6=(X^2+3*Y^2)*(X^4-3*X^2*Y^2+9*Y^4)
=(X^2+3*Y^2)*(X^4+6*X^2*Y^2+9*Y^4-9*X^2*Y^2)
=(X^2+3*Y^2)*((X^2+3*Y^2)^2-(3*X*Y)^2)
=(X^2+3*Y^2)*(x^2-3*X*Y+3*Y^2)*(X^2+3*X*Y+3*Y^2)
ãšïŒã€ã®ç©ã§äœãçŽããã
A^5-B^5=(A-B)*(A^4+A^3*B+A^2*B^2+A*B^3+B^4)
ã§ããã
A=5*X^2,B=Y^2ãšçœ®ãçŽããš
(5*X^2-Y^2)*(625*X^8+125*X^6*Y^2+25*X^4*Y^4+5*X^2*Y^6+Y^8)
=(5*X^2-Y^2)*(25*X^4 - 25*X^3*Y + 15*X^2*Y^2 - 5*X*Y^3 + Y^4)*(25*X^4 + 25*X^3*Y + 15*X^2*Y^2 + 5*X*Y^3 + Y^4)
ãšããïŒã€ã®ç©ã®åœ¢ã«äœãå€ããããã
ããã§
A^7+B^7=(A+B)*(A^6-A^5*B+A^4*B^2-A^3*B^3+A^2*B^4-A*B^5+B^6)
ã§ã¯ãããA,Bãé©åœã«çœ®ãçŽãããšã§
ïŒã€ã®ç©ã§äœã£ã圢ã«çŽããŠã»ããã
No.1409GAI8æ30æ¥ 18:46
4ã€ã ãšç°¡åãªã®ã§ãã¡ããã©3ã€ã®å æ°ããšããããšã§ãããïŒ
ãããªãã°äŸãã°
A=X^3+1, B=Y^3-1 ãšããã°
A^7+B^7=(X^3+1)^7+(Y^3-1)^7
=(X+Y)(X^2-XY+Y^2)
{(X^18-X^15Y^3+X^12Y^6-X^9Y^9+X^6Y^12-X^3Y^15+Y^18)
+7(X^15-X^12Y^3+X^9Y^6-X^6Y^9+X^3Y^12-Y^15)
+21(X^12-X^9Y^3+X^6Y^6-X^3Y^9+Y^12)+35(X^9-X^6Y^3+X^3Y^6-Y^9)
+35(X^6-X^3Y^3+Y^6)+21(X^3-Y^3)+7}
No.1410ãããã8æ30æ¥ 22:31
ãªãã»ã©ïŒ
ãã®çºæ³ã§ããããã®ãã
å
šãé¢ä¿ãããŸãããäžã®ç¬¬ïŒé
ç®ãæžãçŽããš
(X^18+Y^18) - X^3*Y^3*(X^12+Y^12)+X^6*Y^6*(X^6+Y^6)-X^9*Y^9 +
7*{ (X^15-Y^15) -X^3*Y^3*(X^9-Y^9) +X^6*Y^6*(X^3-Y^3)} +
21*{(X^12+Y^12) -X^3*Y^3*(X^6+Y^6) +(X^3-Y^3)+X^6*Y^6} +
35*{ (X^9-Y^9) -X^3*Y^3*(X^3-Y^3) +(X^6+Y^6)-X^3*Y^3} +
7
ãªããã¡ããçšæããŠããã®ã
A=7*X^2,B=Y^2ãšçœ®ããŠåºæ¥ã
823543*X^14+Y^14=(7*X^2+Y^2)*(117649*X^12 - 16807*Y^2*X^10 + 2401*Y^4*X^8 - 343*Y^6*X^6 + 49*Y^8*X^4 - 7*Y^10*X^2 + Y^12)
=(7*X^2+Y^2)
* (343*X^6 - 343*Y*X^5 + 147*Y^2*X^4 - 49*Y^3*X^3 + 21*Y^4*X^2 - 7*Y^5*X + Y^6)
ããããããããã* (343*X^6 + 343*Y*X^5 + 147*Y^2*X^4 + 49*Y^3*X^3 + 21*Y^4*X^2 + 7*Y^5*X + Y^6)
ãªãåŒã§ããã
ãšãªãããããã
No.1411GAI8æ31æ¥ 07:01
åã³ç³ãèš³ãªãã®ã§ãã
ãã®æ£å€è§åœ¢ãã©ãã©ã倧ããããŠè¡ã£ãæãã©ããããããã®ãè¿·ã£ãŠããã®ã§
次ã®åé¡ãèããŠé ãããã
æ£1000è§åœ¢ã®å³åœ¢ããããšããã
ãã®ä»»æã®é ç¹3ãæãéžãã§äœãããäžè§åœ¢ã®å
è§ãå
šéšæŽæ°è§ãšãªã
é ç¹3ãæã®éžã³æ¹(çµåã)ã¯å
šéšã§äœéãããããæ±ããŠæ¬²ããã
äœãé ç¹ã«ã¯åºæã®çªå·ãæ¯ãåœãŠãããŠãããã®ãšããŸãã
ã§ããã
æ£2024è§åœ¢,æ£2345è§åœ¢ã§ãæ±ããŠæ¬²ããã
No.1397GAI8æ25æ¥ 06:18
æ£1000è§åœ¢
1000=2^3Ã5^3ã180÷(2^2Ã5)=9ãš2Ã5^2=50ã¯äºãã«çŽ ãªã®ã§
æŽæ°è§ã«ãªãããã«ã¯é ç¹ã50nå(ååšè§9n°)åäœã§äœ¿çšããªããã°ãªããªãã
âŽ(1000÷50)C3Ã50=57000éã
æ£2024è§åœ¢
2024=2^3Ã11Ã23ã180÷2^2=45ãš2Ã11Ã23=506ã¯äºãã«çŽ ãªã®ã§
æŽæ°è§ã«ãªãããã«ã¯é ç¹ã506nå(ååšè§45n°)åäœã§äœ¿çšããªããã°ãªããªãã
âŽ(2024÷506)C3Ã506=2024éã
æ£2345è§åœ¢
2345=5Ã7Ã67ã180÷5=36ãš7Ã67=469ã¯äºãã«çŽ ãªã®ã§
æŽæ°è§ã«ãªãããã«ã¯é ç¹ã469nå(ååšè§36n°)åäœã§äœ¿çšããªããã°ãªããªãã
âŽ(2345÷469)C3Ã469=4690éã
ã€ãŸãæ£Nè§åœ¢ã®å Žåã¯
g=gcd(N,180)ãšããŠgC3Ã(N/g)éãïŒãã ãgïŒ3ã®ãšã0éãïŒ
ãšããããšã§ããã
No.1398ãããã8æ25æ¥ 08:50
æ£ïŒïŒïŒïŒè§åœ¢ã«ã€ããŠãïŒèŸºã«å¯Ÿããååšè§ã¯ãïŒ/ïŒïŒãªã®ã§ãïŒïŒåã®ãŸãšãŸãããšã«æŽæ°è§ãšãªãã
ãã£ãŠãèªç¶æ°ïœãïœãïœã«å¯ŸããŠãïŒïœïŒïŒïœïŒïŒïœïŒïŒïŒïŒãããããïœïŒïœïŒïœïŒïŒïŒ
å転ãããŠéãªãè§£ïŒïœïŒïœïŒïœïŒã¯åäžèŠããŠãæäœæ¥ã§è§£ãæ±ãããšãïŒïŒéã
ãã£ãŠãäžè§åœ¢ã®éžã³æ¹ã¯ãïŒïŒÃïŒïŒïŒïŒïŒïŒïŒïŒïŒïŒïŒéãïŒãšãªãã
ïŒããããããã®çµæãšäžèŽããŠãå®å¿ããŸããïŒ
No.1399HP管çè
8æ25æ¥ 11:30 äžè¬ã«æ£nè§åœ¢ããã
ãã®ä»»æã®çžç°ãªã3é ç¹A,B,Cãéžãã§äžè§åœ¢ABCãã€ãããšã
å
è§ã®ãã¹ãŠãæŽæ°åºŠ(1Â°ã®æŽæ°å)ãšãªããããªäžè§åœ¢ã§ãã
ããšãèµ·ãã3ç¹ã®éžã³æ¹ã¯ããããäœéããããïŒ
(1)n=14
(2)n=15
(3)n=16
No.1386GAI8æ24æ¥ 08:35
(2)ã¯
æ£15è§åœ¢ã®ã©ã®3é ç¹ãéžãã§ãããã®3ç¹ã§äœãããäžè§åœ¢ã®ãã¹ãŠã®å
è§ã¯æŽæ°åºŠã«ãªããã
15C3=455éã
ãšãªããããªæ°ãããŸããã
ããç§ã®åéãã§ããããææäžããã
No.1390ãããã8æ24æ¥ 13:16
ïŒïŒïŒïŒïŒïŒãèšç®ããŠã¿ãŸãããïŒç¹ã®éžã³æ¹ãåé¡ãªã®ã§ãååãè£è¿ãã§éãªãäžè§åœ¢ãç°ãªããšèŠãªããŠããã
ïŒïŒïŒãæ£ïŒïŒè§åœ¢ã®ïŒèŸºã«å¯Ÿããååšè§ã¯ãïŒïŒÂ°ã§ãããããçµã¿åãããŠäžè§åœ¢ãäœãããšã«ãªãã
ãã£ãŠãïŒïŒåã®é ç¹ããïŒã€ã®é ç¹ãéžã¶å Žåã®æ°ã¯ã153ïŒïŒïŒïŒïŒéãïŒã
ïŒåœåãèãéããããŠããããšã«æ°ã¥ããä¿®æ£ããŸããã
ïŒïŒïŒãæ£ïŒïŒè§åœ¢ã®ïŒèŸºã«å¯Ÿããååšè§ã¯ãïŒïŒïŒïŒïŒÂ°ã§ãããããçµã¿åãããŠäžè§åœ¢ãäœãã«ã¯ã
ïŒïŒïŒïŒïŒïŒïŒãïŒïŒïŒïŒïŒïŒïŒãïŒïŒïŒïŒïŒïŒïŒã®çµã¿åãã§äžè§åœ¢ãäœãããã
ããã£ãŠãæ±ããå Žåã®æ°ã¯ãïŒïŒÃïŒïŒïŒïŒïŒéãïŒ
No.1391HP管çè
8æ24æ¥ 14:53 (2)ã¯455(éã)ã®çµåãã§ããäºäººãšãæ£è§£ã§ãã
(3)ã¯ç§ã®è§£ãšç®¡ç人ãããšã¯ç°ãªã£ãŠããŸãã
ã§ããããã®48éãã¯å
·äœçã«é ç¹ã®éšåã{1,2,3,,16}
ãšãããšããã©ã®é ç¹ã®3ã€ãéžãã§ããã®ãã瀺ããŠãããŸãããã
No.1392GAI8æ24æ¥ 18:37
å
šãèªä¿¡ã¯ãããŸãããïŒïŒïŒã
é ç¹ãïŒãïŒãã»ã»ã»ãïŒïŒãšããå ŽåãïŒïŒïŒïŒïŒïŒïŒã衚ãäžè§åœ¢ãšããŠ
ïŒïŒïŒãšãïŒïŒ10ãšããã»ã»ã»ã§ãâ ïŒïŒïŒïŒâ ïŒïŒïŒïŒïŒïŒÂ°ãâ ïŒïŒïŒïŒïŒïŒÂ°
ãšãªããŸãã
No.1393HP管çè
8æ24æ¥ 20:07 倿¥åãèãããšãã«ãä»»æã® 2 é ç¹éã«ã§ããäžå¿è§ãå¶æ°åºŠã«ãªãã°ãããšèããŸãã
(1)
360/14 ãæŽæ°åããŠå¶æ°ãäœãã«ã¯ 7 ã®åæ°ãæãããããªããæ£ã® 7 ã®åæ° 3 ã€åèšã§ 14 ã«ã¯ã§ããŸããã
ãã£ãŠ 0 éãã
(2)
360/15 ãæŽæ°åããŠå¶æ°ãäœãã«ã¯ä»»æã®æŽæ°ã§ãããçµå± A,B,C ãéè€ããªãããã«ä»»æã«éžã¹ã°ããã§ãã
ãã£ãŠ 15P3 = 2730 éãã
(3)
360/16 ãæŽæ°åããŠå¶æ°ãäœãã«ã¯ 4 ã®åæ°ãæãããããªããæ£ã® 4 ã®åæ° 3 ã€åèšã§ 16 ã«ãªãã®ã¯ 4,4,8 ãšããçµã¿åããã®ã¿ã
ã€ãŸãçŽè§äºç蟺äžè§åœ¢ãäœããããããŸããã
A ãçŽè§ãªãã®ã 16*2 = 32 éããB ãš C ã«ã€ããŠãåãåæ°ããã®ã§ãå
šéšã§ 32*3 = 96 éã
##ã3é ç¹ãéžãã§äžè§åœ¢ãã€ãããã®ã§ã¯ãªããã3é ç¹A,B,Cãéžãã§äžè§åœ¢ABCãã€ãããåé¡ã§ããããç¹ã®ååãå
¥ãæ¿ããã°å¥ç©ãšãã¹ãã ãšæããŸãã
No.1394DD++8æ24æ¥ 20:27
(1)ã¯90°ã®è§åºŠã¯äœãããïŒ1,2,9ã®é ç¹ãªã©)ä»ã®å
è§ã¯æŽæ°ã«ãªããªããçµå±0(éã)
(2)ã¯åºé¡ã®æ3ç¹ãäœæ°ã«A,B,Cãšèšã£ãŠããŸã£ãã®ã§DD++ããã®è§£éãèµ·ãã£ãã(ãã質åãããšDD++ãããæ£ããã)
ãã¡ããæã£ãŠããã®ã¯ã15åã®é ç¹ã®3ã€ã®çµåãã幟ã€åãããïŒ
ã®ã€ããã§èããŠããã®ã§15C3=455(éã)ã§ãé¡ãããŠãããŸãã
(3)ã¯çŽè§äºç蟺äžè§åœ¢ãªããæ¡ä»¶ãæºããã®ã§ããããé ç¹1,2,3,,16
ããã®3ã€ã®é ç¹ã®éžã³æ¹ã¯åé ç¹ã«90°ã®éšåãããå Žåã®16ïŒéã)
ãšããäºå®ã§ããã
æ£nå€è§åœ¢ãšããã®é ç¹ã®ä»»æã®3ç¹ãçµãã§äœãäžè§åœ¢ã®3ã€ã®å
è§ãã©ããæŽæ°è§ãšãªããã®ã
n=5 -->åå
è§ã¯36Â°ã®æŽæ°å
n=6 -->åå
è§ã¯30Â°ã®æŽæ°å
n=9 -->åå
è§ã¯20Â°ã®æŽæ°å
n=10 -->åå
è§ã¯18Â°ã®æŽæ°å
n=12 -->åå
è§ã¯15Â°ã®æŽæ°å
n=15 -->åå
è§ã¯12Â°ã®æŽæ°å
n=18 -->åå
è§ã¯10Â°ã®æŽæ°å
n=20 -->åå
è§ã¯9Â°ã®æŽæ°å
n=30 -->åå
è§ã¯6Â°ã®æŽæ°å
n=36 -->åå
è§ã¯5Â°ã®æŽæ°å
ãèµ·ããããã§ããã
èšç®ãããŠåããŠæ°ä»ããŸããã
No.1396GAI8æ24æ¥ 22:18
aãšbã¯äºãã«çŽ ãªæ£ã®æŽæ°ãkã¯2以äžã®æŽæ°ãnã¯abã®åæ°ã§ããæ£ã®æŽæ°ãšããŸãã
以äžã®Î£ã¯Î£[x[1]=1ïœïœ]Σ[x[2]=1ïœn]âŠÎ£[x[k]=1ïœn]ã®æå³ãšããŸãã
f(m)=e^(2Ïi x[1]x[2]âŠx[k]/m)ãšããŸã(i=â-1)ã
Σf(a)*Σf(b)/Σf(n)ã®å€ãæ±ããŠäžããã
No.1389ã¡ãã£ãšé«äŸ¡ãªã³ãŒããŒè±8æ24æ¥ 10:55
åéãã ã£ãããã¿ãŸãããããã忝ã 0 ã«ãªããŸãããïŒ
No.1395DD++8æ24æ¥ 20:30
çµåæ³åãšã¯
ããæŒç®âã«å¯Ÿã
(aâb)âc=aâ(bâc)
ããã€ãæãç«ã€ããšãæãã
ããã§ä»éåMã®æŒç®ã
Mã®äºã€ã®å
ã«å¯ŸãMã®å
äžã€ã察å¿ãããèŠå
f:MÃMâMãžã®åå
f(a,b)=aâbãã(â(a,b)âMÃM, âaâbâM )
ã§å®çŸ©ããããšã«ããã
ããŠãã®æ
(1)Mã®å
ã2åã§ããæ
MÃMã®å
ã¯2^2=4åã§MÃMããMãžã®ååã¯MÃMã®åå
ã«å¯Ÿã
2éãããè¡ãå
ãæå®ããã®ã§ãå
šéšã§2^(2^2)=16(éãïŒã®ååã
èããããã
ã§ã¯ãã®äžã§çµåæ³åãæºããååã¯äœéããããïŒ
(2)Mã®å
ã3åã§ããæ
å
šéšã§3^(3^2)=19683(éã)ã®ååã®äžã§
çµåæ³åãæºããååã¯äœéããããïŒ
(3)Mã®å
ã4åã§ããæ
å
šéšã§4^(4^2)=4294967296(éã)ã®ååã®äžã§
çµåæ³åãæºããååã¯äœéããããïŒ
No.1382GAI8æ20æ¥ 06:37
(1)ã¯ãïŒéããšãªããŸããã
No.1383HP管çè
8æ20æ¥ 21:59 ããæ¬ãèªãã§ãããšãããã®ååãšçµåæ³åã®çµåãã«ã€ããŠã®èšè¿°ãèªãã§
å®éã©ããªååïŒæŒç®)ãæ¡ä»¶ãæºããã®ããç¥ããããªããMã®èŠçŽ ã2ã€ã®å Žåã«
å
šéš(16éã)ãå
šãŠãã§ãã¯ãããã管ç人ãããšåæ§ã«8éãã§ããããšãå®éšãã
èŠã€ããããŸããã
ã§ããããåãã£ãŠãããããšã¯ã©ãããŠãèŠã€ããããªããæ¬¡ã®Mã®èŠçŽ ã3åã®å Žåã¯
å
šéšã§19683éããããã®ã§ãäœãšãã³ã³ãã¥ãŒã¿ãå©çšããŠã«ãŠã³ãããªãéãåãããªã
ãšæããã®ããã°ã©ã ãã©ãèšèšããã°å¯èœãªã®ããšããããã詊è¡é¯èª€ãç¹°ãè¿ããŠçµã¿äžããŠ
ãããŸãããïŒäœæ¥ãçµã¿æ¹ãåãããæªæŠèŠéã®é£ç¶ã§ãããïŒ
ãã£ãšããã§æ±ãŸãã®ã§ã¯ãªãããšæãããããã°ã©ã ã§èšç®ããçµæã113éãã§ããã
Mã®èŠçŽ ã4ãªã3492éãã«ãªããŸããã(çµæãåºããŸã§éåæéãããããŸãããïŒ
Mã®èŠçŽ ã2ã®å Žåã«èŒã¹ããã®æ¯çãæ¥µç«¯ã«å°ãããªã£ãã®ã§ãã®çµæã¯èªä¿¡ããããŸããã§ããã
ãã®å
ãã®8,113,3492ãäŸã®OEISã§æ€çŽ¢ãããš
A023814ããããããŸããã
ã§ããã®ãµã€ãã§ã®èª¬ææã§ã¯äœãçµåæ³åãªãèšè¿°ã¯ãªããæ°ã¯äžèŽããããããæ±ããæ°ã
瀺ããã®ãããŸãã¡èªä¿¡ããããŸããã
äœæ¹ããã®æ°ãç€ºãæ£ããæ°å€ãèŠã€ããŠè²°ãããã®ã§ãã
ãããã®æ°å€ãæ£ãããªãçµåæ³åãæãç«ã€ãšã¯ãšãŠãçããçŸè±¡ã§ãããšèªèããªããš
ãããªããã®ã ãšæããã
No.1384GAI8æ21æ¥ 20:20
GAIãã
>ãã®å
ãã®8,113,3492ãäŸã®OEISã§æ€çŽ¢ãããš
>A023814ããããããŸããã
>ã§ããã®ãµã€ãã§ã®èª¬ææã§ã¯äœãçµåæ³åãªãèšè¿°ã¯ãªããæ°ã¯äžèŽããããããæ±ããæ°ã
>瀺ããã®ãããŸãã¡èªä¿¡ããããŸããã
è±èªã®æå³ãæ€çŽ¢ãããšã
associative : ãæŒç®ãªã©ããçµåçãªãçµååŸïŒ»æ³åïŒœãæºãã
binary operation : äºé
æŒç®
ãããã®ã§ã
" Number of associative binary operations on an n-set "
ã¯
ãèŠçŽ æ°nã®éåã«ãããçµåæ³åãæºããäºé
æŒç®ã®æ°ã
ãšãªã£ãŠGAIãããç¥ããããã®ãã®ãã®ã§ã¯ãªãã§ããããïŒ
No.1385ããã²ã8æ21æ¥ 23:34
åèš1332ä»¶ (æçš¿217, è¿ä¿¡1115)