245813719612412378787994384765625
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èšç®æ©ã§ãã«ãŒããã©ãŒã¹çã«ç¢ºèªããã®ã§ãããïŒ
No.1615Dengan kesaktian Indukmu2023幎12æ28æ¥ 00:10
ã€ã³ãã®äºå¹³æ¹åå®çããèããã°ãçŽ å æ°å解ã®åœ¢ã§ãããªãæèšç®ã§ããããŸããã
2024/4 = 506 = 2*11*23 ãªã®ã§ã
4ã§å²ããš1äœãçŽ æ°ã«å°ããé ã« 23-1, 11-1, 2-1 ãææ°ãšããŠäžããã°ããã ãã§ãã
ã€ãŸã N = 5^22 * 13^10 * 17 ã§ãããã
âŠâŠããèªäœã幎æãã«åºé¡ããã°ããã£ãã®ã§ã¯ïŒ
No.1616DD++2023幎12æ28æ¥ 01:20
DD++ããã埡æ瀺ããŸããšã«æé£ãããããŸãã
OEISã§ã¿ãããã®ã«ãæ€çŽ¢ã«ããããªããŠåŸçããŠãããŸããã
幎è³æšæ¶ã®ãã©ã€ã³ã°ã¯ããããšãããã¯ãªã¹ãã¹ãéããã®ã§ããããªããšïŒãéã
No.1617Dengan kesaktian Indukmu2023幎12æ28æ¥ 18:23
URL ãã¿ã€ãããŸããã
https://oeis.org/A016032/b016032.txt
No.1618Dengan kesaktian Indukmu2023幎12æ28æ¥ 20:11
Dengan kesaktian Indukmuãããã玹ä»ããããµã€ãã®é¢é£ãªã³ã¯
http://www.math.aoyama.ac.jp/~kyo/sotsuken/2019/sotsuron_2019_Shoda.pdf
ãèªãã§ããã
ã¬ã³ãé¢æ°Î(z),ãªã€ã©ãŒã®ã¬ã³ãæ°Î³,ãŒãŒã¿é¢æ°Î¶(z)ã®é¢ä¿åŒãšããŠ
Î(1)=1
Î'(1)=-γ
Î''(1)=Ï^2/6+γ^2=ζ(2)+γ^2
ã®å»¶é·ãšããŠ
Î'''(1)=-(2*ζ(3)+3*γ*ζ(2)+γ^3)
ã玹ä»ãããŠããã®ã§æŽã«ç¶ããæ¢ã£ãŠãããš
Î''''(1)=6*ζ(4)+8*γ*ζ(3)+3*ζ(2)^2+6*γ^2*ζ(2)+γ^4
(ãªã³ã¯å
ã®ãã®éšåã¯èšç®ãã¹ãèµ·ããŠãããšæãããŸãã)
æŽã«
Î'''''(1)=-(24*ζ(5)+20*γ*ζ(4)+20*γ^2*ζ(3)+20*ζ(2)*ζ(3)+15*γ^2*ζ(2)^2+10*γ^3*ζ(2)+γ^5)
çã
ã®é¢ä¿åŒãçãŸããŠããããã§ãã
ãããŸã§ã¯äžå¿èšç®æ©ã«ããåãå€ãäžããŠããããšã確èªããŸãããïŒæåŸã®éšåã®ç¢ºèªãäžèš)
gp > gamma'''''(1)
%80 = -117.83940826837742425256416965496496106
äžæ¹
gp > -(24*zeta(5)+30*Euler*zeta(4)+20*Euler^2*zeta(3)+20*Euler^2*zeta(3)\
+20*zeta(2)*zeta(3)+15*Euler*zeta(2)^2+10*Euler^3*zeta(2)+Euler^5)
%81 = -117.83940826837742425256416965496496106
æ®å¿µãªããζ(3),ζ(5)ã«ã¯Ïãå«ãŸããŠããªãã®ã§Î''(1)ãæãçµã³ã€ããæ¥çåã匷ãããã§ãã
ãŸã
γ=1/2*(ζ(2)-1)+2/3*(ζ(3)-1)+3/4*(ζ(4)-1)+4/5*(ζ(5)-1)+
ãªãåŒã«ãåŒãä»ããããŸãã
(åè)
gp > sumpos(n=2,(n-1)/n*(zeta(n)-1))
%83 = 0.57721566490153286060651209008240243103
gp > Euler
%84 = 0.57721566490153286060651209008240243104
No.1613GAI2023幎12æ24æ¥ 17:09
次ã®å®ç©åã®å€ã¯äœïŒ
(1)â«[0â3]floor(x^2)dx
(2)â«[0â3]ceil(x^2+floor(x))dx
(3)â«[1/Ïâ1/2]log(floor(1/x))dx
(4)â«[e^âÏâ(âÏ)^e^2]ceil(x)dx
No.1595GAI2023幎12æ11æ¥ 01:19
åçã§ã¯ãããŸãããç³ãèš³ãããŸããã
æè¿ããããªã®ãèŠãããŸããŠç®ãäžžãããŠãã次第ã§ãã
â«[0â1](1/x -floor(1/x))dx = 1 -γ
x=0 ã®ä»è¿ã§æ¿ããæ¯åããé¢æ°ã®å®ç©åãªã®ã§ã©ããã£ãŠæ±ããã®ããšææ¡æãéŠã§ãã
ãªããwolfalpha ã§ã¯çããŠãããŸããã§ããã
No.1598Dengan kesaktian Indukmu2023幎12æ12æ¥ 16:45
â«[0â1](1/x-floor(1/x))dx
=â«[1/2â1](1/x-1)dx+â«[1/3â1/2](1/x-2)dx+â«[1/4â1/3](1/x-3)dx+âŠ
=lim[nââ]{â«[1/nâ1](1/x)dx-Σ[k=2ïœn](1/n)}
=lim[nââ]{logn-Σ[k=2ïœn](1/n)}
=-lim[nââ]{Σ[k=2ïœn](1/n)-logn}
=1-lim[nââ]{Σ[k=1ïœn](1/n)-logn}
=1-γ
ãšãªããŸããã
No.1599ãããã2023幎12æ12æ¥ 17:25
â«[x=1ââ](1/floor(x)-1/x)dx=γ
ãšãªãããã§ããã
No.1601GAI2023幎12æ13æ¥ 08:15
Euler's constant (or the Euler-Mascheroni constant), gamma.
ãšèšãããγã«ã€ããŠãWikipediaã§ã®èšäºãèªãã§ã¿ãã
γãšååšçÏãšã®é¢ä¿ãåãã£ãŠããªããšããèšè¿°ãèŠãããã
äŸãã°Ïãšèªç¶å¯Ÿæ°ã®åºeãšã¯ãããã€ãªãé¢ä¿åŒã¯ãã°ãã°èŠãããšã¯ãããã
ããããã°Î³ãšÏã¯ããŸãèŠãããšã¯ãªãã£ãã
ããã§ãªãããªãã®ããšæ¢ãåã£ãã
Îé¢æ°ã§
Î(1/2)=âÏ
Î'(1)=-γ
ãšã¬ã³ãé¢æ°ã§è¡šçŸã§ã
ãŸãããŸããŸ
γ^2+Ï^2/6=Î''(1)=â«[x=0ââ]e^(-x)*(log(x))^2dx
ãæç«ããããšãçºèŠããã(A081855åç
§)
ããã¯ïŒã€ãçµã³ã€ãã倧ããªé¢ä¿ã§ã¯ãªããããïŒ
äœæ¹ãä»ã«äœãïŒã€ãçµã¶é¢ä¿åŒããåç¥ã®æ¹ã¯ãæãäžããã
No.1602GAI2023幎12æ13æ¥ 21:51
æ¬æ¥ã¿ãããã®ã§ãã
â«[x=0ââ] ((sin(x)*log(x))/x)dx = -γ*Ï/2
ãªã®ã ããã§ãã
ã埡åèã
https://mathlog.info/articles/FB8gF9bmpb3LJ5CDZBzo
No.1608Dengan kesaktian Indukmu2023幎12æ22æ¥ 12:59
èšç®æ©ã§ç¢ºèªããããã¿ãªåãæ°å€ã確èªããŸããã
sinãšlogã®çµåãïŒ
æ°åŠã£ãŠäžæè°ã§é¢çœãã
No.1610GAI2023幎12æ23æ¥ 07:44
ä»»æã®äžè§åœ¢ã¯ããã®é ç¹ããåäžååšäžã«ãåããããšãã§ããã
éè§ãªè§ãæã€å¹³è¡å蟺圢ã¯ãåäžååšäžã«ãåããããšãã§ããªãã
ä»»æã®åžäºè§åœ¢ã¯ããã®é ç¹ããåäžã®ååšäžã«ãåããããšãã§ããã
(ãã®ãŸãŸã§ã¯ç¡çå¹³è¡å蟺圢ãå«ããããæ¡ä»¶ãç·©ããŠãè§A,B,C,D,
Eãšåã䞊ã³ã®äºè§åœ¢ãååã§ã¯ãªã)ã¯å¯èœã§ããããïŒ
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No.1597ks2023幎12æ12æ¥ 10:37
åžäºè§åœ¢ABCDEã«å¯ŸããŠãâ AïŒaãâ BïŒb,â C=c,â D=d,â E=e
眮ããŸãã
a=Ξ1ïŒÎ2ïŒÎ3 +0 + 0
b=ïŒïŒÎ2ïŒÎ3ïŒÎ4+0
c=ïŒïŒïŒïŒÎ3ïŒÎ4ïŒÎ5 ïŒAïŒÎïŒïŒÎïŒïŒÎïŒïŒÎïŒïŒÎïŒïŒ
d=Î1ïŒïŒïŒïŒïŒÎ4ïŒÎ5ãããåãã¯ãã«
e=Î1ïŒÎ2ïŒïŒïŒïŒïŒÎ5
å·¡åè¡åAã¯ãæ£åã§ãéè¡åãæã¡ã
äžããããïŒa,b,c,d,e)ã«å¯ŸããŠãïŒÎïŒïŒÎïŒïŒÎïŒïŒÎïŒïŒÎïŒïŒ
ã決ãŸããŸããäœå³ãã§ãããå¿é
ã§ãããïŒè§åºŠãåãåãã§ããã°ãïŒ
ååšäžã«ãäžç¹AïŒä»®ïŒãé©åœã«ãšããå·ŠãããÎ1ïŒâ BAC,ÎïŒïŒâ CAD,
ÎïŒïŒâ DAEãšããŠãç¹B,C,D,Eãå®ãããÎïŒïŒâ ECA,ÎïŒïŒâ ADBã«ãªãããã«ãæ¹ããŠç¹AãBEã®éã«å®ããã°ãã§ãããããããŸããããèªä¿¡ããããŸããã
No.1603ks2023幎12æ14æ¥ 16:25
æ£æ¹åœ¢BCDEãšæ£äžè§åœ¢ABCãšãäœå³ããŸãã
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眮ã§ããªããšæãããŸãããã©ããç§ã®é¡æèªã¿éããªã®ã§ããããïŒ
No.1605Dengan kesaktian Indukmu2023幎12æ15æ¥ 22:59
åäŸãããããšãããããŸãã
ãã®å ŽåãÎïŒãããã€ãã¹ã«ãªããŸããã
æ£æ°å€ã§ããåæ¯ãïŒã®å Žåãäœå³ãé£ãããã§ããã
No.1606ks2023幎12æ18æ¥ 09:54
察è§ã®åããïŒïŒïŒÂ°ãªãã°ãåã«å
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ä»»æã®äºèæïŒãã³ã¿ã°ã©ãïŒã¯ãåã«å
æ¥ãããããšãã§ããã
ïŒé·ãã¯åãã§ãªããšããè§ã®äžŠã³ããåããšããæå³ã§ïŒ
ä»»æã®å
èæããå¯èœã
No.1607ks2023幎12æ20æ¥ 13:20
ä»æ©ã¯ãã1+2+3+4+ã»ã»ã»=ãŒ1/12ãã ããã§ãã
2023幎11æ29æ¥ NHKç·åååŸ11:00ã11:30
ãèŠéããªãã
åæŸéã¯ã
äžåç®12æ 2æ¥ïŒåïŒEãã¬ååŸïŒïŒïŒïŒïœååŸ10:00
äºåç®12æ6æ¥ïŒæ°ŽïŒEãã¬ååïŒïŒïŒïŒïœåå1:25
ã ããã§ãããªã³ã¯ã貌ã£ãŠãããŸãã
æ¥é±ã¯ãBSDäºæ³ãã ããã§ãã
No.1574ããããã¯ã¡ã¹ã2023幎11æ29æ¥ 07:05 ä»æ©ã¯ããBSDäºæ³ãã ããã§ãã
2023幎12æ6æ¥ NHKç·åååŸ11:00ã11:30
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ã·ãŒãºã³ïŒã¯ããã§çµããã ããã§ãã
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äžåç®12æ 9æ¥ïŒåïŒEãã¬ååŸ9:30ïœååŸ10:00
äºåç®12æ13æ¥ïŒæ°ŽïŒEãã¬åå0:55ïœåå1:25
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No.1591ããããã¯ã¡ã¹ã2023幎12æ6æ¥ 07:08 ä»æ©ã¯ããçŽ æ°ãã ããã§ãã
2023幎12æ13æ¥ NHKç·åååŸ11:00ã11:30
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äžåç®12æ 16æ¥ïŒåïŒEãã¬ååŸ9:30ïœååŸ10:00
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10æãã12æãŸã§ãšãªã£ãŠãããŸããã®ã§ã
No.1600ããããã¯ã¡ã¹ã2023幎12æ13æ¥ 07:13
亀ç¹ã®ãªãçµã³ç®ã®ãåŒã¯ã©ããªããŸããïŒ
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No.1579ks2023幎11æ30æ¥ 15:00
ç§ã¯ãã®æ¹é¢ã«ã€ããŠã¯ãŸã£ããç¡ç¥ã§ãããã©ãã調ã¹ãçµæããå ±åãããŠãã ããã
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â 亀ç¹ã®ãªãçµã³ç®ã®ã¢ã¬ããµã³ããŒå€é
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ã«ã€ããŠã®èª¬æã以äžã® PDF ã«ãããŸãã
http://www.f.waseda.jp/taniyama/mathsciknot/reports/23.pdf
以äžã§ãã
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No.1580Dengan kesaktian Indukmu2023幎12æ1æ¥ 22:09
ããããšãããããŸãã
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ïŒã«ãªããªãã®ã§ãå°ããŸãããæ±ãæ¹ããããããã§ããã
No.1592ks2023幎12æ6æ¥ 10:38
埡åèã
ã¢ã¬ããµã³ããŒå€é
åŒã»ããæåã©ããã®å€é
åŒããçµã³ç®ããšã«çŽ¹ä»ããŠãããµã€ãããããŸãã
泚:httpsã«å¯Ÿå¿ããŠãããhttpãªãµã€ãã®ããäžéšã®ãã©ãŠã¶ã§ã¯ã¢ã¯ã»ã¹ã§ããªãããšããããŸãã
http://katlas.math.toronto.edu/wiki/The_Rolfsen_Knot_Table
ããšãã°èªæãªçµã³ç®ã§ããã°ã
äžèšããŒãžã®ãKnots with 7 or fewer crossingsãã«ãªããã åçµã³ç®ã®ãã¡ãã0_1ãã®ãªã³ã¯ãèžãã°
http://katlas.math.toronto.edu/wiki/0_1
ã®ããŒãžã«é£ã³ãŸãããã®ããŒãžã¯èªæãªçµã³ç®ã®ããŒãžã§ãã
ãPolynomial invariantsãã®æ¬ã«ç®ããã
ããã«ãã
ãAlexander polynomialãããã1ã
ã§ããããšããã
èªæãªçµã³ç®ã®ã¢ã¬ããµã³ããŒå€é
åŒã¯ 1 ãšãããããã§ãã
ãŸããåæ§ã«ã㊠3_1 ã®ãªã³ã¯ãèžãã°trifoliate leaves (äžã€è)ã®çµã³ç®ã®ããŒãžã«é£ã³ãŸãã
http://katlas.math.toronto.edu/wiki/3_1
ã¢ã¬ããµã³ããŒå€é
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t +1/t -1
ãšãªãããã§ããã
ãã®çµã³ç®ã¯ãè£è¿ããšã¢ã¬ããµã³ããŒå€é
åŒãéã圢ã«ãªãã®ã§ã¯ãšãŒããããšèšæ¶ããŠããã®ã§ããããã¡ãã«ã€ããŠã¯ä»åãæ¡å
ããã¢ã¯ã»ã¹æ¹æ³ã§ã¯æ€çŽ¢ã§ããŸããã§ãããã容赊ãã ããã
No.1593Dengan kesaktian Indukmu2023幎12æ6æ¥ 17:45
ç¬ããªãæ°åŠã§çŽ¹ä»ãããŠããã¢ã¬ããµã³ããŒå€é
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èªæãªçµã³ç®ã¯è²ã
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åŒãæ§æãããŠããŸãã¿ããã§ããã
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çåºæ¥ãŠããŸãã
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åŒãšãªããšæãããŸãã
No.1594GAI2023幎12æ6æ¥ 19:01
âããã¯ã©ãããæ°ã§ãããïŒ
0.202030508âŠ
é»åçšåºŠã¯OKã§ãããæ€çŽ¢ãWolframAlphaãªã©ã®ã«ã³ãã³ã°ã¯çŠæ¢ã§ãã
No.1587ãããã2023幎12æ3æ¥ 16:09
10000x = 2020.30508âŠâŠ
101x = 20.4050813âŠâŠ
å·®ãåŒã
9899x = 1999.9
ãã£ãŠ
x = 19999/98990
æµç³ã«äžèªç¶ããªïŒ
No.1588DD++2023幎12æ3æ¥ 21:36
gp > Z=0.202030508;
é»åçšåºŠãªãèš±ãããŠããã®ã§
gp > for(n=1,10,print(n";"n*Z))
1;0.20203050800000000000
2;0.40406101600000000000
3;0.60609152400000000000
4;0.80812203200000000000
5;1.0101525400000000000
6;1.2121830480000000000
7;1.4142135560000000000
8;1.6162440640000000000
9;1.8182745720000000000
10;2.0203050800000000000
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ã ãã
â2/7ã蟺ãããªïŒ
No.1589GAI2023幎12æ4æ¥ 06:09
â2/7ããæ£è§£ãã§ãã
â2ã2æ¡ãã€ã«åºåããš7ã®åæ°ã4ã€ãé£ç¶ããŠããããšãã7ã§å²ã£ãŠã¿ãããªãã
å²ã£ããããŸããŸãã£ãããã颚ã®æ°åãåºãŠããŸããã
No.1590ãããã2023幎12æ4æ¥ 06:46
n ïŒ 1 ãšããŸãã
n次ã®å€é
åŒ P(x) ã«ã€ããŠ
æ¹çšåŒ P(x) = 0 ã
n åã®å®æ°è§£ãæã¡ãé解ã¯ãªããã®ãšããŸãã
ãŸããP(x) ã®å°é¢æ°ã Q(x) ãšããŸãã
ãã®ãšããq ã
q = Σ (1 /Q(x))
(äœã n åã®å®æ°è§£ã«ã€ããŠç·åãããã®ãšããŸãã )
ã§å®çŸ©ããŸãã
質åããããŠãã ããã
q 㯠任æã® P(x) ã«ã€ããŠ
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â»ææã§ã¿ãããŠ
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ããšãã°
P(x) = x^3 -3*x -8*x -4
ã§è©ŠããŠã¿ããšãã
q = (1/(16-3*2^(5/2))) +(1/(16+3*2^(5/2))) +1 = 0
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No.1575Dengan kesaktian Indukmu2023幎11æ29æ¥ 16:58
>q 㯠任æã® P(x) ã«ã€ããŠ
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次ã®ãã¡ã€ã«ã®67ããŒãžãã芧ãã ããã
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https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv32n5.pdf
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ãCrux Mathematicorum 2006幎9æå·ã
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No.1576at2023幎11æ29æ¥ 19:48
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No.1577Dengan kesaktian Indukmu2023幎11æ30æ¥ 11:09
q = 0 ã¯ãããšèªæãããªãã§ããããïŒ
æ¹çšåŒ P(x) = t ã® n åã®å®æ°è§£ã®åèšã S(t) ãšãããšã
ïŒãã ã t ã¯ãã®æ¹çšåŒã n åã®ç°ãªãå®æ°è§£ãæã€ç¯å²ãåãïŒ
q ãšããã®ã¯ Sâ(0) ã®ããšãªããã§ããã
nâ§2 ã§ããã°è§£ãšä¿æ°ã®é¢ä¿ãã S(t) ã¯ããããå®æ°é¢æ°ã§ãã
No.1578DD++2023幎11æ30æ¥ 13:43
DD++ããããã€ããã€ãæé£ãããããŸãã
埡æ瀺ãé ããŸãããšããã®
ãq ãšããã®ã¯ Sâ(0) ã
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No.1581Dengan kesaktian Indukmu2023幎12æ1æ¥ 22:14
dengan ãã
ãããªæãã§äŒãããŸãã§ããããïŒ
æ¹çšåŒ P(x) = 0 ã®è§£ãå°ããé ã« x = a[k] ïŒ1âŠkâŠnïŒãšããŸãã
æ²ç· y = P(x) ãšçŽç· y = 0 ããå (a[k],0) ã«äº€ç¹ãäœã£ãŠããæãã§å³ãæãæµ®ãã¹ãŠãã ããã
ãããããçŽç· y = 0 ãã»ãã®ãããã«äžäžã«ããã㊠y = t ã«ç§»åãããŸãã
ãããšãåäº€ç¹ (a[k],0) ãå°ã移åã㊠y 座æšã t ã«ãªããŸããã
ãã®ãšããå亀ç¹ã®ããè¿ãã§ã¯æ²ç·ã¯ã»ãŒåŸã Q(a[k]) ã®çŽç·ã«ãªã£ãŠããã亀ç¹ã¯åœç¶ããããªããããã«ç§»åããŸãã
ãããã£ãŠãx 座æšã®å€åã¯ãy 座æšã®å€å t ã® 1/Q(a[k]) åãšãªã£ãŠããŸãã
ãšããããšã¯ãã亀ç¹ã® x 座æšã®åèš S(t) ã¯ãS(0) ãã qt ã ãå¢å ãããããã§ããã
å®ã¯ãã®æã ãèŠãã° q ã¯åŸ®åä¿æ° Sâ(0) ã®å®çŸ©ãã®ãã®ã§ãã
No.1582DD++2023幎12æ2æ¥ 06:38
ãªãªãªïŒïŒïŒ
æé£ãããããŸããDD++ããã
ç§ã«ãèŠããŸããã
No.1583Dengan kesaktian Indukmu2023幎12æ2æ¥ 06:53
nãèªç¶æ°ãšãããšã
2^(2*n) + 2^(2*n+3) + 2^p
ãå¹³æ¹æ°ãšãªãèªç¶æ°pããã äžã€ååšãããšããã
ãã®pã®å€ã¯äœãïŒ
No.1564GAI2023幎11æ27æ¥ 07:00
(n,p)=(1,6),(2,8),(3,10),(4,12),âŠã§æãç«ã¡ãŸãã®ã§ãpã¯äžã€ã«æ±ºãŸãããåé¡ãæ£ãããªããšæããŸãã
ãšæããŸããããã²ãã£ãšããŠãäžè¡ç®ã¯ãèªç¶æ°nã«å¯ŸããŠããšããæå³ã§ãçããp=2n+4ãšããããšã§ããããã
No.1565ãããã2023幎11æ27æ¥ 08:21
GAIããŸãããããããŸãããã«ã¡ã¯ã
ããããããŸãšåãã§ããã
2^(2n)+2^(2n+3)+2^p=a^2ãšãããšã
2^(2n)+8*2^(2n)+2^p=a^2
9*2^(2n)+2^p=a^2
2^p=a^2-9*2^(2n)
2^p=(a+3*2^n)(a-3*2^n)
巊蟺ã¯æ£ã ãããa-3*2^n>0
2^p=(a+3*2^n)(a-3*2^n)
ãããb+3,b-3ã2^c,2^dã«ãªãã®ã¯ã
b+3=2^cãããb=2^c-3
b-3=2^dãããb=2^d+3
WolfRamAlphaã«ãããšãæŽæ°è§£ã¯b=5,c=3,d=1ã®1çµãããªãã
ãã£ãŠãa=5*2^nã ãšããŠa-3*2^n=2*2^n
ã ãšããŠa+3*2^n=8*2^n
ãããã£ãŠã
2^p=(a+3*2^n)(a-3*2^n)
2^p=16*(2^n)* (2^n)=16*2^(2n)=2^4*2^(2n)=2^(2n+4)
ããã«p=2n+4
å€åãçŽ å æ°å解ã®ïŒææ§ããšã¿ã€ãã«ããããŠã解æ³ã¯ééã£ãŠãããšããããŸãã
No.1566ããããã¯ã¡ã¹ã2023幎11æ27æ¥ 15:04
2^(2*n) + 2^(2*n+3) ã 9*
2^(2*n) ãšæžããŠããªãã®ãäžèªç¶ãªã®ã§ãåé¡ã誀èšããŠããã®ã§ãããã
2^(2*n) + 2^(n+3) + 2^p
ãæ£ããåŒã§ãçã㯠p=4 ãšãã§ãããã
No.1567DD++2023幎11æ27æ¥ 17:31
2^(2*n) + 2^(n+3) + 2^p
ã®å Žåã¯ãpãä»»æã®nã«å¯Ÿããå®æ°ãªãã°p=4ãããªãã§ãã
ãä»»æã®nãããªãããŠãnã«äŸåããŠããããªãã°nãå¥æ°éå®ã§p=(3n+5)/2ãšãã解ããããŸããã
No.1568ãããã2023幎11æ27æ¥ 18:52
ããããã¯ã¡ã¹ããããããã«ã¡ã¯ã
ïŒ2^p=(a+3*2^n)(a-3*2^n)
ãããb+3,b-3ã2^c,2^dã«ãªãã®ã¯ã
b+3=2^cãããb=2^c-3
b-3=2^dãããb=2^d+3
WolfRamAlphaã«ãããšãæŽæ°è§£ã¯b=5,c=3,d=1ã®1çµãããªãã
ããã¯æèšç®ã§ããããŸããã
b+3=2^cãããb=2^c-3
b-3=2^dãããb=2^d+3
âŽ2^c-3ïŒ2^d+3ãâŽ2^c-2^d=6ãâŽ2^(c-1)-2^(d-1)=3
å³èŸºãå¥æ°ãªã®ã§å·ŠèŸºãæ£ã®å¥æ°ã§ãd-1=0,c-1=2ã®å Žåãããªãã
âŽc=3,d=1ãâŽb=2^3-3=5
ãã£ãŠãæŽæ°è§£ã¯b=5,c=3,d=1ã®1çµãããªãã
ãŸãã2^p=(a+3*2^n)(a-3*2^n)ããã巊蟺ãå¶æ°(pâ 0ãšãã)ããå³èŸºãå¶æ°ã§ã
aã¯å¶æ°ããa=2m(mã¯æŽæ°)ãšçœ®ããšã2^p=(2m+3*2^n)(2m-3*2^n)
âŽ2^(p-1)=(m+3*2^(n-1))(m-3*2^(n-1))
ãããç¹°ãè¿ãäºã«ãªãã®ã§ãåãã«a=b*2^nïŒnä¹ãããªããšå³èŸºã¯å¥æ°ã«ãªã£ãŠããŸãïŒãšçœ®ããšã
2^p=(b*2^n+3*2^n)(b*2^n-3*2^n)
âŽ2^(p-2n)=(b+3)(b-3)
ãã£ãŠãb+3=2^cïŒb-3=2^dãšçœ®ãã®ã§ãããïŒp-2n>0ïŒ
No.1569å£ããæ2023幎11æ27æ¥ 19:18
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2^(2*n)+2^(2*n+3)+2^p=m^2 (m;æŽæ°)
ãšãããš
2^p=m^2-2^(2*n)*(1+2^3)
=m^2-(2^n*3)^2
=(m-3*2^n)*(m+3*2^n)
ããã«çŽ å æ°å解ã®äžææ§ãã
m-3*2^n=2^sâ
m+3*2^n=2^tâ¡
ãæºãã(s<t)èªç¶æ°s,tãååšããã
ãã ãs+t=pâ¢
â¡-â ãã
3*2^(n+1)=2^t-2^s=2^s*(2^(t-s)-1)
ããã«2^sã¯å¶æ°ãã2^(t-s)-1=3ã§ãªããã°ãªããªãã
ãã£ãŠ
2^(t-s)=2^2ããt-s=2
ãã®ãšãs=n+1
ããããt=s+2=n+3
â¢ããp=2*n+4
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No.1570GAI2023幎11æ27æ¥ 19:21
å£ããæããŸãããã°ãã¯ã
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GAIããŸãããã°ãã¯ã
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No.1571ããããã¯ã¡ã¹ã2023幎11æ27æ¥ 19:35
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n äŸåã®è©±ããããªããn ãå¥æ°éå®ã§ p = 3n-5 ããããŸãããn = 7 㧠p = 15 ã®ãããªããªãç¹æ®ãªè§£ããããŸãã
ãŸãããªãã«ãã誀èšã§ã¯ãªãã£ãããã§ãããã©ãã
GAI ãã
9*4^n ãšããç°¡çŽ ãªè¡šèšã«ããããããã 2^(2*n)+2^(2*n+3) ãšããè¡šèšã«ããçç±ã¯ãªãã ã£ãã®ã§ãããïŒ
No.1572DD++2023幎11æ27æ¥ 21:33
管ç人ããŸã®è§£æ³ã¯ããã§ããŠããŸããã
No.1573ããããã¯ã¡ã¹ã2023幎11æ28æ¥ 14:09
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No.1560ã«ã«ãã¹2023幎11æ26æ¥ 18:15
åäŸãããã®ã§ããããšãèšããªããšæããŸãããã®å Žåã¯ãããŸã㟠30°ã§ããïŒïŒïŒã
No.1561HP管çè
2023幎11æ26æ¥ 18:41 ããã¯äºç蟺äžè§åœ¢ã§ãªããšæãç«ã¡ãŸããã
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No.1562ãããã2023幎11æ26æ¥ 18:41
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No.1563ã«ã«ãã¹2023幎11æ26æ¥ 20:50