OEIS/A003828
There seem to be more than 19 solutions by Seiji Tomita.
- euler413.narod.ru
- www.maroon.dti.ne.jp has really huge solutions. list as of 2017-07-20
- database.txt on euler.fr
- Robert Gerbicz on uhunt.onlinejudge.org
- www.maroon.dti.ne.jp has really huge solutions.
Seiji Tomita's List as of 2017-07-20
18796760 15365639 2682440 20615673 Noam Elkies, 1986
414560 217519 95800 422481 Roger Frye, 1988
16921802132217020 15075240668820384 128805698258642759 16774794902382238 Seiji Tomita, 03/13/2006
4480680305 72584786800 1062203384 23661446513
582665296 260052385 186668000 589845921 Seiji Tomita, 03/13/2006
3134081336 2448718655 664793200 3393603777 Seiji Tomita, 01/28/2007
47886740272114976 8813425670440240 56827813308111785 62940516903410601 Seiji Tomita, 8/13/2008
3579087147375440 14890026433468471 18565945114216720 20249506709579721 Seiji Tomita, 8/13/2008
4987588419655 2480452675600 502038853976 5062297699257 Seiji Tomita, 5/15/2008
275156240 219076465 630662624 638523249 Seiji Tomita, 7/16/2017
2767624 1390400 673865 2813001 Allan MacLeod,1997
1670617271 632671960 50237800 1679142729 Seiji Tomita, 03/13/2006
22495595284040 7592431981391 27239791692640 29999857938609 Seiji Tomita, 03/13/2006
5821981400 15355831360 140976551 15434547801 Seiji Tomita, 10/24/2007
130064300991400 440804942580160 514818101299289 573646321871961 Seiji Tomita, 9/15/2008
8332208 5507880 1705575 8707481 D.J. Bernstein,2001
894416022327 125777308440 2032977944240 2051764828361 Seiji Tomita, 7/15/2017
1166705840 859396455 588903336 1259768473 Robert Gerbicz, ... 2008
41714673255 18125123544 34169217200 46055390617 Seiji Tomita, 7/16/2017
1171431921806295280 5113654767499398206 4048310673060768880 5557992180974240706 Andrew Bremner, 2013
11289040 8282543 5870000 12197457 D.J. Bernstein,2001
1662997663 1237796960 686398000 1787882337 Robert Gerbicz, ...
54772209880944552 50049879917257109 16178554328069755 62586521087452988 Andrew Bremner, 2013
338211440 403510290 572637088 953161234
17111129720 52289667920 55479193841 64244765937 Seiji Tomita, 7/20/2017
18776929334105 23449050222680 12035933588696 25866132798297 Seiji Tomita, 7/20/2017
27450160 146627384 108644015 156646737 Juergen Rathmann, 6/1/2007
14173720 12552200 4479031 16003017 D.J. Bernstein,2001
817201061520 2095956175810 2452045365504 2734283895746 Andrew Bremner, 2013
4707813440 7813353720 11988496761 12558554489 Andrew Bremner, 2013
1841160 121952168 122055375 145087793 Juergen Rathmann, 5/31/2007
1041572957760 535914713672 187577183625 1059621884297 Seiji Tomita, 7/16/2017
41084175 31669120 2164632 44310257 Robert Gerbicz, 11/08/2006
1593513080 1553556440 92622401 1871713857 Robert Gerbicz, ...
16281009 7028600 3642840 16430513 D.J. Bernstein,2001
769321280 606710871 558424440 873822121 Robert Gerbicz, ...
65932985 42878560 10409096 68711097 Robert Gerbicz, 11/08/2006
106161120 87865617 34918520 117112081 Robert Gerbicz, 11/02/2006
70 Digits (Elkies, 1988)
from ams.org:
9033964577482532388059482429398457291004947925005743028147465732645880^4 + 4417264698994538496943597489754952845854672497179047898864124209346920^4 + 1439965710648954492268506771833175267850201426615300442218292336336633^4 = 9161781830035436847832452398267266038227002962257243662070370888722169^4