RESTA's Algorithm

This is the page which tracks the work done on:
(6,1,6) (6,1,7)
(6,2,3) (6,2,4) (6,2,5)
(8,1,9) (8,1,10)
(8,2,7) (8,2,8)
(8,3,6) (8,3,7)
(10,1,13) (10,1,14)
(10,2,11) (10,2,12) (10,2,13)
(10,3,11) (10,3,12) (10,3,13)
(10,4,11) (10,4,12)
(10,5,12) (10,5,13)

The method used for this search is based on Giovanni Resta's work, and largely improved by Jean-Charles Meyrignac.
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3rd October 2000: Matthias Koehler found a solution for (6,2,5) above 40,000 !

6th July 2000:
First solutions to (6,1,7) collected with EulerNet ! Congratulations Greg Childers !!!

20th May 2000: Nuutti Kuosa found (8,1,9) !!!!
11678=10948+10408+5608+5588+3668+3488+2848+2718+1908

2nd February 2000: Tommy Nolan found (10,3,12) !
120+44+22=116+102+90+85+65+51+51+41+37+23+5+2

30th January 2000: Pascal Gelebart found the smallest (10,5,13):
44+44+22+15+14=47+31+31+26+23+16+12+9+7+6+5+5+5
44+44+36+35+11=46+39+38+34+30+30+30+24+24+18+18+14+9

26th January 2000: Nuutti Kuosa found (10,2,12):
112+99=109+103+83+79+72+59+59+52+20+15+5+5

58 distinct solutions for (6,2,5) have been found !

(6,2,5) 1117+770=1092+212+602+861+84 (Giovanni Resta, Edward Brisse)
(6,2,5) 2041+691=1893+1468+1246+1407+1302 (Giovanni Resta)
(6,2,5) 2441+752=2096+1266+1484+1239+2184 (Giovanni Resta)
(6,2,5) 2827+151=1488+390+1281+2653+2296 (Giovanni Resta)
(6,2,5) 2959+2470=2481+850+2954+798+420 (Giovanni Resta)
(6,2,5) 5585+3850=3010+1060+4305+420+5460 (Larry Hays, Tommy Nolan, divisible by 5)
(6,2,5) 6623+323=642+363+6615+434+2912 (Larry Hays, Tommy Nolan)
(6,2,5) 8905+347=5489+534+2576+2499+8820 (Tommy Nolan)
(6,2,5) 8969+5203=2379+478+9023+2604+2520 (Tommy Nolan)
(6,2,5) 9551+9451=4884+3943+3976+8589+10080 (Tommy Nolan)
(6,2,5) 9612+7271=7446+5118+6580+6279+9198 (Tommy Nolan)
(6,2,5) 9707+6277=9675+5531+3640+5796+4536 (Tommy Nolan)
(6,2,5) 10205+3455=9465+7340+6230+7035+6510 (Tommy Nolan, divisible by 5)
(6,2,5) 12205+3760=10480+6330+7420+6195+10920 (Tommy Nolan, divisible by 5)
(6,2,5) 12272+2459=8283+9144+1400+11522+7434 (Tommy Nolan)
(6,2,5) 12287+8470=6622+2332+9471+924+12012 (Tommy Nolan, divisible by 11)
(6,2,5) 13417+5933=11378+10698+70+4641+11403 (Tommy Nolan)
(6,2,5) 13903+5317=13788+6026+1232+8295+1827 (Tommy Nolan)
(6,2,5) 14135+755=7440+1950+6405+13265+11480 (Tommy Nolan, divisible by 5)
(6,2,5) 14521+10010=11193+2756+7826+14196+1092 (Tommy Nolan, divisible by 13)
(6,2,5) 14795+12350=12405+4250+14770+3990+2100 (Tommy Nolan, divisible by 5)
(6,2,5) 15149+6914=14520+810+10675+10444+6006 (Gerben Dirksen)
(6,2,5) 15627+1865=14196+13608+5385+4032+565 (Edward Brisse)
(6,2,5) 15905+10519=14679+13759+9534+3822+2482 (Edward Brisse)
(6,2,5) 16103+9111=6253+2004+13755+8484+14868 (Hugues MacKaulay)
(6,2,5) 16159+10532=10273+11016+15442+3234+11760 (Hugues MacKay)
(6,2,5) 16160+1865=11470+4329+4984+15792+1008 (Hugues MacKay)
(6,2,5) 16315+8749=11682+11140+11375+7119+15246 (Hugues MacKay)
(6,2,5) 16867+14786=17790+2502+9821+2912+9786 (Hugues MacKay)
(6,2,5) 17737+16043=17646+14574+14261+3255+2590 (Hugues MacKay)
(6,2,5) 18989+13090=18564+14637+10234+3604+1428 (Torbjörn Alm, divisible by 17)
(6,2,5) 19168+1747=10088+8214+5299+18984+10584 (Frank Clowes)
(6,2,5) 19869+10673=9783+2088+1925+19866+9324 (Frank Clowes)
(6,2,5) 20111+15059=13812+2499+18879+14854+15680 (Larry Hays)
(6,2,5) 20173+15459=20469+1170+13118+11550+5355 (Larry Hays)
(6,2,5) 20235+1690=11706+11472+19915+5754+10542 (Larry Hays)
(6,2,5) 20273+17527=16182+8892+4221+20755+5348 (Larry Hays)
(6,2,5) 21223+14630=20748+16359+11438+4028+1596 (Larry Hays, divisible by 19)
(6,2,5) 22451+7601=20823+16148+15477+14322+13706 (Larry Hays, divisible by 11, 03/31/2000)
(6,2,5) 23192+20259=22932+19170+16874+13629+7602 (Larry Hays)
(6,2,5) 24781+125=23457+20046+6951+2968+214 (Larry Hays, 05/04/2000)
(6,2,5) 25153+6036=25116+11297+6798+6090+6006 (Jean-Charles Meyrignac)
(6,2,5) 25309+19441=23996+22302+11532+8897+2067 (Jean-Charles Meyrignac)
(6,2,5) 25360+4407=25020+15372+13524+10542+5015 (Jean-Charles Meyrignac)
(6,2,5) 25691+17710=25116+19803+13846+4876+1932 (Jean-Charles Meyrignac, divisible by 23)
(6,2,5) 25951+4901=25750+15486+7203+3906+3031 (Jean-Charles Meyrignac, 06/08/2000)
(6,2,5) 26143+21591=27132+16625+8871+5622+966 (Jean-Charles Meyrignac, 06/13/2000)
(6,2,5) 26435+21913=27702+5887+3339+2568+1274 (Jean-Charles Meyrignac, 06/20/2000)
(6,2,5) 26533+8983=24609+19084+18291+16926+16198 (Jean-Charles Meyrignac, divisible by 13, 06/23/2000)
(6,2,5) 26797+12368=24794+22764+11539+5148+1386 (Jean-Charles Meyrignac, 07/03/2000)
(6,2,5) 26851+8272=24024+23056+16324+13926+13629 (divisible by 11, Jean-Charles Meyrignac, 07/03/2000)
(6,2,5) 27081+15688=25116+20762+20664+8322+6135 (Jean-Charles Meyrignac, 04/22/2000)
(6,2,5) 27925+19250=27300+21525+15050+5300+2100 (divisible by 25, Jean-Charles Meyrignac, 07/17/2000)
(6,2,5) 28314+3211=27531+19006+17580+12096+4452 (Kevin O'Hare)
(6,2,5) 28537+2038=28112+16702+16602+12519+3360 (Kevin O'Hare)
(6,2,5) 29040+22271=29804+16590+5748+4914+2625 (Kevin O'Hare, 03/30/2000)
(6,2,5) 29384+17515=28518+22088+16128+9828+1355 (Kevin O'Hare, 05/10/2000)
(6,2,5) 29875+28496=31584+25158+7536+2632+1901 (Kevin O'Hare, 05/10/2000)
(6,2,5) 30038+4607=26726+26310+17650+12831+12474 (Jean-Charles Meyrignac, Hugues MacKay, 04/22/2000)
(6,2,5) 40261+31165=41489+20472+9642+8351+7224 (Matthias Koehler, 11/03/2000)

COMMENT: Since the program is very slow above 30,000, (6,2,4) will be started above 30,000.

25 distinct solutions for (6,1,7).
(6,1,7) 1141=1077+894+702+474+402+234+74 (Lander, Parkin and Selfridge,1966)
(6,1,7) 1645=430+1299+1560+864+702+618+150
(6,1,7) 1757=1402+195+1494+1248+1242+1200+804
(6,1,7) 2009=664+345+1944+1506+522+198+90
(6,1,7) 2023=1136+345+1902+1548+1320+240+30
(6,1,7) 2471=2228+1017+1956+1728+1668+552+510
(6,1,7) 3073=2830+1761+2568+1446+1086+996+576

(6,1,7) 34781=19229+33354+8190+21252+24360+10920+18480 (Jean-Charles Meyrignac, Wannes de Smedt)
(6,1,7) 38191=34223+9102+33726+16506+7266+6216+12432 (Jean-Charles Meyrignac, Wannes de Smedt)
(6,1,7) 39779=11834+17955+37506+31752+22008+12516+2940 (Jean-Charles Meyrignac, Wannes de Smedt)
(6,1,7) 54347=33376+32748+19467+48846+3150+2100+46032 (Wannes de Smedt)
(6,1,7) 59819=7574+9402+8715+51744+48342+44310+42966 (Wannes de Smedt)
(6,1,7) 63631=54018+39088+25263+54138+48090+23268+1344 (Wannes de Smedt)
(6,1,7) 66029=25582+51891+58758+51366+38892+12264+20916 (Wannes de Smedt)
(6,1,7) 67681=49968+2800+8001+65100+33138+35574+32046 (Wannes de Smedt)
(6,1,7) 70513=57978+60550+18417+57246+13314+26040+21672 (Wannes de Smedt)
(6,1,7) 78919=38730+57890+40761+75978+38598+26124+13776 (Wannes de Smedt)
(6,1,7) 89797=27852+58450+11739+83580+67704+60018+10038 (Wannes de Smedt)
(6,1,7) 97081=20568+86632+37401+81522+21798+69930+31752 (Wannes de Smedt)
(6,1,7) 108805=75420+81221+94038+17178+53676+85512+65856 (Wannes de Smedt)
(6,1,7) 123943=111783+106204+73122+66402+29442+12684+6294 (Greg Childers, 07/06/2000)
(6,1,7) 125945=116382+87276+85680+82306+81447+62664+41622 (Greg Childers, 07/06/2000)
(6,1,7) 130783=120330+100408+85665+83034+72030+65688+29190 (Greg Childers, 07/06/2000)
(6,1,7) 141709=122675+114198+112350+79884+75180+52164+24060 (Greg Childers, 07/09/2000)
(6,1,7) 144175=131292+114772+107793+41370+16452+11550+6048 (Greg Childers, 07/11/2000)

COMMENT: Since the left terms are always multiples of 7 and a solution to (6,1,6) cannot be a multiple of 7, the search of (6,1,7) will be done on NON multiples of 7 !

1 solution has been found for (8,1,9):
(8,1,9) 1167=1094+1040+560+558+366+348+284+271+190 (Nuutti Kuosa, 05/20/2000)

2 solutions have been found for (8,1,10):
(8,1,10) 235=226+184+171+152+142+66+58+34+16+6 (Nuuti Kuosa, 04/05/1999)
(8,1,10) 705=678+552+513+456+426+198+174+102+48+18 (Janne Penttilä, divisible by 3)

7 solutions have been found for (8,2,8):
(8,2,8) 129+95=128+92+86+82+74+57+55+20 (Randy Ekl)
(8,2,8) 251+165=242+192+190+174+136+117+85+12 (Nuutti Kuosa)
(8,2,8) 275+75=264+228+180+155+154+125+62+24 (Emrecan Dogan, 01/27/2000)
(8,2,8) 321+179=288+281+258+228+168+98+85+68 (Emrecan Dogan, 01/29/2000)
(8,2,8) 325+44=322+232+162+116+60+52+48+5 (Emrecan Dogan, 01/29/2000)
(8,2,8) 387+285=384+276+258+246+222+171+165+60 (Emrecan Dogan, divisible by 3, 02/16/2000)
(8,2,8) 397+35=358+330+316+285+269+264+244+128 (Emrecan Dogan, 02/16/2000)
(8,2,8) 415+298=402+324+324+248+200+146+65+64 (Emrecan Dogan, 02/19/2000)

18 solutions have been found for (8,3,7):
(8,3,7) 108+68+5=102+88+37+88+52+26+6 (JC Meyrignac, 1997)
(8,3,7) 125+100+31=120+113+19+46+6+36+12 (Larry Hays)
(8,3,7) 135+69+3=123+118+109+73+58+4+8 (Larry Hays, 01/03/2000)
(8,3,7) 147+68+30=128+128+51+126+2+88+96 (Larry Hays, 01/03/2000)
(8,3,7) 161+161+20=172+137+103+58+36+22+22 (Larry Hays, 01/03/2000)
(8,3,7) 171+35+6=168+121+119+98+78+68+48 (Larry Hays, 01/03/2000)
(8,3,7) 180+128+87=168+148+137+6+88+144+32 (Larry Hays, 01/03/2000)
(8,3,7) 203+110+10=190+181+118+98+98+66+22 (Larry Hays, 01/05/2000)
(8,3,7) 229+180+94=226+188+91+146+66+132+76 (Larry Hays, 01/05/2000)
(8,3,7) 239+181+103=225+205+177+178+6+90+140 (Larry Hays, 01/09/2000)
(8,3,7) 247+97+85=238+203+151+159+18+48+96 (Larry Hays, 01/09/2000)
(8,3,7) 247+121+95=231+208+196+136+67+29+34 (Larry Hays, 01/09/2000)
(8,3,7) 254+199+49=256+180+145+39+108+110+60 (Larry Hays, 01/09/2000)
(8,3,7) 257+231+120=266+186+141+93+38+164+8 (Larry Hays, 01/09/2000)
(8,3,7) 260+223+133=264+196+184+98+61+23+56 (Larry Hays, 01/09/2000)
(8,3,7) 313+279+225=302+297+216+176+99+77+28 (Larry Hays, 02/18/2000)
(8,3,7) 324+204+15=306+264+264+156+111+78+18 (Larry Hays, 06/03/2000, divisible by 3)
(8,3,7) 328+190+37=314+283+108+74+46+28+16 (Larry Hays, 06/16/2000)

1 solution has been found for (10,1,14)
(10,1,14) 120=115+104+91+80*2+74+63+55+40+35+33+13+10+5 (Torbjörn Alm, 10/14/1999)

1 solution has been found for (10,2,12)
(10,2,12) 112+99=109+103+83+79+72+59+59+52+20+15+5+5 (Nuutti Kuosa, 01/26/2000)
(10,2,12) 135+55=129+115+105+103+83+80+71+71+51+47+15+12 (Victor Pliousnine, 02/29/2000)

1 solution has been found for (10,2,13)
(10,2,13) 51+32=49+43+41+37+28+26+25+15+10*2+9+5+3 (Meyrignac,1997)

1 solution has been found for (10,3,12)
(10,3,12) 120+44+22=116+102+90+85+65+51+51+41+37+23+5+2 (Tommy Nolan, 02/02/2000)

14 solutions have been found for (10,3,13)
(10,3,13) 46+32+22=43+43+27+26+17+16+12+9+9+6+4+3+3 (Meyrignac, 1997)
(10,3,13) 68+66+18=67+61+58+57+54+48+47+43+35+29+25+16+16 (Tommy Nolan, 01/15/2000)
(10,3,13) 70+44+35=65+61+60+51+45+45+34+32+25+12+9+5+3 (Tommy Nolan, 01/15/2000)
(10,3,13) 75+31+11=70+67+62+49+48+29+26+16+16+12+8+4+4 (Tommy Nolan, 01/17/2000)
(10,3,13) 77+54+6=75+63+60+53+50+46+31+29+27+25+24+9+7 (Tommy Nolan, 01/17/2000)
(10,3,13) 79+23+11=78+60+56+54+40+34+30+30+20+15+8+3+1 (Tommy Nolan, 01/17/2000)
(10,3,13) 80+36+22=78+65+60+56+51+42+41+32+27+27+15+9+1 (Tommy Nolan, 01/17/2000)
(10,3,13) 80+66+44=76+70+69+55+53+52+46+42+31+23+21+15+9 (Tommy Nolan, 01/17/2000)
(10,3,13) 86+77+20=85+71+70+67+63+62+45+39+26+19+19+13+12 (Tommy Nolan, 01/19/2000)
(10,3,13) 87+50+44=81+81+54+53+52+47+45+41+39+38+38+31+13 (Tommy Nolan, 01/19/2000)
(10,3,13) 87+77+43=84+74+72+72+64+63+52+38+20+20+17+9+8 (Tommy Nolan, 01/19/2000)
(10,3,13) 89+88+2=94+72+65+49+27+24+24+15+9+3+3+3+3 (Tommy Nolan, 01/22/2000)
(10,3,13) 90+44+42=85+81+70+50+49+47+40+32+29+26+23+15+3 (Tommy Nolan, 01/23/2000)
(10,3,13) 90+76+44=91+65+59+56+54+38+35+32+29+27+13+5+4 (Tommy Nolan, 01/23/2000)

4 solutions have been found for (10,4,12)
(10,4,12) 53+44+44+22=51+49+43+39+29+28+17+17+16+13+7+4 (Eric Bainville, 1999)
(10,4,12) 99+66+44+24=96+81+81+59+57+57+21+20+14+9+5+3 (Greg Childers, 01/13/2000)
(10,4,12) 106+88+88+44=102+98+86+78+58+56+34+34+32+26+14+8 (Greg Childers, 01/19/2000, divisible by 2)
(10,4,12) 112+77+66+66=107+94+90+89+67+67+59+53+49+40+19+7 (Greg Childers, 01/19/2000)

3 solutions have been found for (10,5,13):
(10,5,13) 44+44+22+15+14=47+31+31+26+23+16+12+9+7+6+5+5+5 (Pascal Gelebart, 01/30/2000)
(10,5,13) 44+44+36+35+11=46+39+38+34+30+30+30+24+24+18+18+14+9 (Pascal Gelebart, 01/30/2000)
(10,5,13) 53+44*2+22+3=51+49+43+39+29+28+17*2+16+13+7+4+3 (Victor Pliousnine, 04/17/2000)

Ranges in italic are finished.

Search of (6,1,6) below 2,640,000 (type 3)
 Start Range End Range Searcher Last report Number of solutions found 0 200000 Simon 01/22/2000 0 200000 272580 Yu Guan (Hugues MacKay) 07/17/2000 0 272581 300000 300000 350000 Larry Hays 06/14/2000 0 350000 375012 Tommy Nolan 09/05/2000 375013 400000 Tommy Nolan 400000 404147 Simon 03/16/2000 0 404148 450000 Simon 450000 468864 Jo Yeong Uk 11/03/2000 0 466337 500000 Jo Yeong Uk 500000 502464 Jeffrey Dahmer 04/22/2000 0 502465 600000 Jeffrey Dahmer 600000 700000 Michael Lau

Search of (6,1,7) below 2,640,000 (type 0)
 Start Range End Range Searcher Last report Number of solutions found 0 100000 Wannes de Smedt 12/30/1999 12 100000 123425 Wannes de Smedt 12/30/1999 1 123425 2000000 Reserved EulerNet (Wannes de Smedt)

Search of (6,2,3) below 65,536 (type 20)
 Start Range End Range Searcher Last report Number of solutions found 0 23008 Edward Brisse 03/31/2000 0 23009 65536 Edward Brisse

Search of (6,2,4) below 2,640,000 (type 2)
 Start Range End Range Searcher Last report Number of solutions found 0 21000 Flowerek 03/03/2000 0 21000 100000 Flowerek

Search of (6,2,5) below 65,000 (type 6)
 Start Range End Range Searcher Last report Number of solutions found 0 10000 Tommy Nolan 12/05/1999 12 10000 15000 Tommy Nolan 01/15/2000 9 15000 15150 Gerben Dirksen 12/22/1999 1 15150 16000 Edward Brisse 01/29/2000 2 16000 19000 Hugues MacKay 04/17/2000 7 19000 19900 Frank Clowes 01/09/2000 2 19900 20000 Edward Brisse 02/01/2000 0 20000 21000 Larry Hays 12/16/1999 4 21000 23000 Larry Hays 04/22/2000 2 22999 25000 Larry Hays 05/08/2000 1 25000 27000 Jean-Charles Meyrignac 07/06/2000 10 27000 28000 Jean-Charles Meyrignac 07/20/2000 2 28000 30000 Kevin O'Hare 05/10/2000 5 30000 30420 Hugues MacKay 10/04/2000 1 30421 35000 Hugues MacKay 35000 40000 Mark Uiterwaal 40000 40264 Matthias Koehler 11/03/2000 1 40265 45000 Matthias Koehler 45000 50000 50000 50021 Jean-Charles Meyrignac 03/31/2000 50022 60000 60000 100000

Search of (8,1,9) below 4,096 (type 7) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 959 Nuutti Kuosa 05/22/2000 1 960 Nuutti Kuosa

Search of (8,1,10) below 4,096 (type 1) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 4096 Nuutti Kuosa 2

Search of (8,2,7) below 4,096 (type 8)
 Start Range End Range Searcher Last report Number of solutions found 0 899 Nuutti Kuosa (Alx) 07/23/2000 0 900 4000 Nuutti Kuosa

Search of (8,2,8) below 4,096 (type 4) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 420 Emrecan Dogan 02/19/2000 8 421 2000 Emrecan Dogan 2000 4096

Search of (8,3,6) below 4,096 (type 10) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 432 Leon Deutsch 05/16/2000 0 433 4096 Leon Deutsch

Search of (8,3,7) below 4,096 (type 5) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 328 Larry Hays 06/16/2000 18 329 4096 Larry Hays

Search of (10,1,13) below 10,000 (type 15) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 201 Torbjörn Alm 03/03/2000 202 2000 Torbjörn Alm

Search of (10,1,14) below 10,000 (type 9) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 152 Torbjörn Alm 01/27/2000 1 153 2000 Torbjörn Alm

Search of (10,2,11) below 10,000 coming soon !
 Start Range End Range Searcher Last report Number of solutions found 0 2000 Victor Pliousnine

Search of (10,2,12) below 10,000 (type 16)
 Start Range End Range Searcher Last report Number of solutions found 0 116 Nuutti Kuosa 01/28/2000 1 117 141 Victor Pliousnine 02/28/2000 1 142

Search of (10,2,13) below 10,000 (type 11) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 80 Victor Pliousnine 01/22/2000 1 81 2000

Search of (10,3,11) below 10,000 (type 22)
 Start Range End Range Searcher Last report Number of solutions found 0 186 Tommy Nolan 02/14/2000 187 2000 Tommy Nolan

Search of (10,3,12) below 10,000 (type 17)
 Start Range End Range Searcher Last report Number of solutions found 0 142 Tommy Nolan 02/27/2000 1 143 2000 Tommy Nolan

Search of (10,3,13) below 10,000 (type 12) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 80 Tommy Nolan 01/17/2000 8 81 85 Tommy Nolan 86 87 Tommy Nolan 01/19/2000 3 88 2000 Tommy Nolan 01/23/2000 3

Search of (10,4,11) below 10,000 (type 18)
 Start Range End Range Searcher Last report Number of solutions found 0 119 Greg Childers 120 152 Greg Childers 03/12/2000 153 500 Greg Childers

Search of (10,4,12) below 10,000 (type 13) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 113 Greg Childers 01/19/2000 4 114 500 Greg Childers

Search of (10,5,12) below 10,000 (type 19) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 2000 Pascal Gelebart 54 56 Victor Pliousnine 09/01/2000 57 2000 Victor Pliousnine

Search of (10,5,13) below 10,000 (type 14) CANCELLED
 Start Range End Range Searcher Last report Number of solutions found 0 44 Pascal Gelebart 01/30/2000 2 45 500 Pascal Gelebart

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