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2019-11-06, 09:39   #34
AndrewWalker

Mar 2015
Australia

2·41 Posts

Thanks Ed, I really hope the new pairs are useful, and would love to hear how they are useful!

In the future I'd like to post the pairs list more often, but without creating a new post each time. Is there a way to create a sticky post I can update, or a link to the file I can update? The file with each pair factored takes more work so will be less often.

Andrew

Quote:
 Originally Posted by garambois I just got back from vacation. What a pleasant surprise ! Thank you very much for these new lists. They will replace the old ones in our programs... Paul Zimmermann's program is running right now. No other cycle of length other than 2 until now, which would be added to the one of length 6 announced above.

 2019-11-13, 09:32 #35 garambois     Oct 2011 24·3·7 Posts Andrew, Paul Zimmermann's program is running on my computer. He found a cycle 2 that is not in your list of 910 pairs. 0 -217294*I - 668517 = [[18*I + 23, 1], [6*I + 11, 1], [2*I + 1, 2], [2*I + 3, 1], [93*I + 52, 1]] Factors of N(z) = 494131661725 = 5^2 * 13 * 157 * 853 * 11353 1 -882506*I + 263517 = [[120*I + 29, 1], [6*I + 1, 1], [2*I + 1, 2], [12*I + 245, 1]] Factors of N(z) = 848258049325 = 5^2 * 37 * 15241 * 60169 Jean-Luc
 2019-11-14, 10:10 #36 AndrewWalker     Mar 2015 Australia 1228 Posts Thanks Jean, confirm it's a new pair will add it to my lists! This looks like it is just outside the range of one of my searches for (1+2*I)^2 *4 factors. Will try to rediscover it! Andrew
 2019-11-20, 10:05 #37 garambois     Oct 2011 24×3×7 Posts Andrew, Paul Zimmermann found with his own computer, two new cycles 2 that are not in your list of 910 911 pairs. 0 -637121*I - 388928 = [[53*I + 28, 1], [12*I + 23, 1], [22*I + 15, 1], [3*I + 2, 1], [2*I + 1, 2]] Factors of N(z) = 557188157825 = 5^2 * 13 * 673 * 709 * 3593 1 -455119*I + 708608 = [[4*I + 1, 1], [2*I + 1, 2], [20*I + 27, 1], [1215*I + 44, 1]] Factors of N(z) = 709258601825 = 5^2 * 17 * 1129 * 1478161 0 -13357*I + 942574 = [[24*I + 1, 1], [3*I + 2, 1], [2*I + 1, 2], [2*I + 15, 1], [142*I + 23, 1]] Factors of N(z) = 888624154925 = 5^2 * 13 * 229 * 577 * 20693 1 -966683*I + 116906 = [[330*I + 29, 1], [4*I + 1, 1], [2*I + 1, 2], [5*I + 2, 1], [5*I + 26, 1]] Factors of N(z) = 948143035325 = 5^2 * 17 * 29 * 701 * 109741 Jean-Luc
 2019-11-25, 07:14 #39 AndrewWalker     Mar 2015 Australia 2×41 Posts Thanks for the updates! I'll add these to my list, have also found a number of others since my last update. I suspect most of those Paul found and I missed are due to the factors being beyond the limits of my current search, so it's good to have a search very different from mine! Please keep an eye out for any which a) Don't have 1 or -I as the unit factor; or b) don't have 1+I, 1+2*I or 1+ 4*I as one of the factors I suspect b) will be found eventually (similar to regular amicable pairs not divisible by 6 or even scarcer not divisible by 30) a) I suspect is true, maybe there is a simple proof? Andrew
2019-11-30, 04:00   #40
AndrewWalker

Mar 2015
Australia

8210 Posts

Thanks again for the updates Paul and Jean-Luc! Have just updated my list with your pairs and a few new ones of mine which takes it to 943 pairs. Have made this 7a, 8 will be at 1000 or more!

As always, any errors, omissions or other problems please let me know!

Andrew
Attached Files
 GaussListMaster7a.txt (39.6 KB, 39 views)

 2019-11-30, 11:14 #41 garambois     Oct 2011 24×3×7 Posts OK, a lot of thanks Andrew.

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