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(ax-n)(ay-n)=n^2
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3^3*5*7=945ã®çŽæ°ã®åæ°ã63ã§æå€
ãªã®ã§2/945ãæå€ïŒè§£ã¯(63+1)/2=32åïŒãšãªãããšãäºæ³ãããŸãã
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3^2*5*7*11=3465, 3^2*5*7*13=4095, 3^2*5*7*17=5355, 3^2*5*7*19=5985,
3^2*5*7*23=7245, 3^2*5*7*29=9135, 3^2*5*7*31=9765, 3^2*5*11*13=6435,
3^2*5*11*17=8415, 3^2*5*11*19=9405, 3^2*5*13*17=9945, 3^2*7*11*13=9009,
3*5^2*7*11=5775, 3*5^2*7*13=6825, 3*5^2*7*17=8925, 3*5^2*7*19=9975,
3*5*7^2*11=8085, 3*5*7^2*13=9555
(4+1)(2+1)^3=135
(135+1)/2=68
ãã
2/3465,2/4095,2/5355,2/5775,2/5985,2/6435,2/6825,2/7245,2/8085,
2/8415,2/8925,2/9009,2/9135,2/9405,2/9555,2/9765,2/9945,2/9975
ã®18éãã§è§£ã68åãšãªãã®ãæå€ã100000æªæºã§ã¯
3^2*5*7*11*13=45045, 3^2*5*7*11*17=58905, 3^2*5*7*11*19=65835,
3^2*5*7*11*23=79695, 3^2*5*7*13*17=69615, 3^2*5*7*13*19=77805,
3^2*5*7*13*23=94185, 3*5^2*7*11*13=75075, 3*5^2*7*11*17=98175,
(4+1)(2+1)^4=405
(405+1)/2=203
ãã
2/45045,2/58905,2/65835,2/69615,2/75075,2/77805,2/79695,2/94185,2/98175
ã®9éãã§è§£ã203åãšãªãã®ãæå€ïŒãããã確èªæžã¿ïŒã§ããã
(è¿œèš)
1000000æªæºã§ã¯
3^2*5*7*11*13*17=765765, 3^2*5*7*11*13*19=855855
(4+1)(2+1)^5=1215
(1215+1)/2=608
ãã
2/765765,2/855855ã®2éãã§è§£ã608åãšãªãã®ãæå€
ãšãªãããã§ãããããã¯æªç¢ºèªã§ãã
No.1984ãããã2024幎7æ2æ¥ 15:24
2/765765=1/x+1/y (xâŠy)
ãæºãã[x,y]ã調ã¹ãŠã¿ãŸããã
M=[[765765], [382883, 293198400495], [382884, 97733055420], [382885, 58639986405], [382886, 41885813970], [382887, 32577940395], [382888, 26654748120], [382889, 22554076545], [382890, 19546917390], [382891, 17247325095], [382893, 13962193245], [382895, 11728303587], [382896, 10859568720], [382899, 8885171295], [382900, 8377469100], [382902, 7518280770], [382905, 6515894385], [382907, 5984015895], [382908, 5749363620], [382910, 5331255930], [382914, 4654319670], [382915, 4511121615], [382920, 3909689784], [382921, 3808149345], [382923, 3620111495], [382925, 3449771325], [382928, 3222339120], [382932, 2961979020], [382935, 2792744955], [382941, 2506348845], [382942, 2464231770], [382943, 2423506995], [382950, 2172220050], [382954, 2050718670], [382956, 1994927220], [382959, 1916709795],
[424710, 3887730], [425425, 3828825], [425799, 3798795], [425880, 3792360], [427245, 3687453], [427350, 3679650], [427635, 3658655],

[626535, 984555], [630630, 974610], [634270, 966042], [634865, 964665], [636480, 960960], [638495, 956403], [645150, 941850], [645645, 940797], [647955, 935935], [651508, 928620], [654381, 922845], [656370, 918918], [658944, 913920], [659022, 913770], [661045, 909909], [663663, 904995], [664020, 904332], [666666, 899470], [668745, 895713], [675495, 883883], [675675, 883575], [680680, 875160], [683298, 870870], [692835, 855855], [693420, 854964], [696150, 850850], [701415, 843115], [701505, 842985], [706095, 836451], [706860, 835380], [711620, 828828], [714714, 824670], [717145, 821457], [718263, 819995], [720720, 816816], [726495, 809523], [729729, 805545], [734825, 799425], [737919, 795795], [740520, 792792], [740740, 792540], [743886, 788970], [749190, 783090], [750057, 782145], [753984, 777920], [759330, 772310]]
#M=608
å
šéšãã¢ããããããšãããã10000åãè¶ããŸããã®ã§ã¢ãããäžæ¢ããŸãã®èŠåãåºãã®ã§éäžããã¶ãã®éšåãçç¥ããŸããã
2/855855ã確èªããŸããã
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No.1985GAI2024幎7æ2æ¥ 17:22
ãã®åŸ1000000æªæºã§ã¯2/765765,2/855855ã®608åãæå€ã§ããããšã¯ç¢ºèªã§ããŸããã
ãããŠã€ãã§ã«10000000æªæºã調ã¹ãŸããã10000000æªæºã§ã¯
3*5*7*11*13*17*19=4849845, 3*5*7*11*13*17*23=5870865, 3*5*7*11*13*17*29=7402395,
3*5*7*11*13*17*31=7912905, 3*5*7*11*13*17*37=9444435, 3*5*7*11*13*19*23=6561555,
3*5*7*11*13*19*29=8273265, 3*5*7*11*13*19*31=8843835, 3*5*7*11*17*19*23=8580495
(2+1)^7=2187
(2187+1)/2=1094
3^4*5*7*11*13*17=6891885, 3^4*5*7*11*13*19=7702695, 3^4*5*7*11*13*23=9324315
(8+1)(2+1)^5=2187
(2187+1)/2=1094
ãã
2/4849845,2/5870865,2/6561555,2/6891885,2/7402395,2/7702695,
2/7912905,2/8273265,2/8580495,2/8843835,2/9324315,2/9444435
ã®12éãã§è§£ã1094åãšãªãã®ãæå€ïŒç¢ºèªæžã¿ïŒã§ãã
No.1986ãããã2024幎7æ2æ¥ 22:50