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Title: Computer Science/Distributed Computing/Projects - Computing Minimum Equal Sums of Like Power Includes client software download, computation records, and project description on its research into mathematical problems.
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Computing Minimum Equal Sums Of Like Power_uacct = "UA-54247-2";urchinTracker(); Computing Minimal Equal Sums Of Like PowersLet's find a power of 6 equal to 6 powers of 6.Join EulerNet !Last updatedIndex11/09/2006FAQ01/22/2002Top ProducersFrequently !Search this site01/05/2003Download09/30/2002Mailing list09/19/2000Solitaire Competition12/31/2002Peg Solitaire tough problems01/13/2003Database11/09/2006K10 search02/22/2003Old results10/09/2002Cheap software01/30/2003Links08/21/2001Identities02/09/2001Theorems01/24/2003Prime solutions09/15/2005Prime database09/15/2005High power solutions04/10/2002Records02/14/2001Progress status03/25/2001Most wanted01/24/2003Resta11/03/2000Project details01/27/2001Taxicab numbers12/18/2002How it works04/02/2000Greetings01/04/2001AVL04/02/2000Scher12/28/2000Morpion Solitaire04/15/2003Knight tours04/25/2003Peg Infos12/30/2002Javascript10/24/2002Dungeon Keeper 211/10/2006This project is dedicated to all those who are fascinated by powers and integers.In the following, k, m, nand every term ai,bj always denotepositive integers.For given k and m, this page summarizesall the known minimal solutions for n of theequation:a1k+ a2k+ ... + amk = b1k+b2k+ ... +bnkwith:a1 >= a2 >= ... >= amb1 >= b2 >= ... >= bna1 > 1m <= nfor example:52 = 42+32 = 25123+13 = 103+93 = 17291584+594 = 1344+1334 = 6353186574224814 = 4145604+2175194+958004 = 318587498400079459203211445 = 1335+1105+845+275 = 61917364224141325+2205 = 140685+62375+50275 = 563661204304422162432236+156+106 = 226+196+36 = 1604265149668+5398+818 = 9548+7258+4818+3108+1588 = 765381793634649192581218Lander, Parkin and Selfridge conjectured in 1966 that:for every k > 3, m + n >= kGiven the power k and the left number of termsm, we are trying to lower the known right number ofterms n.You can find more informations on the detailed page.If you want to participate, go to the download page.Check the EulerNet Top Producers here9th November 2006: Nuutti Kuosa found (8,4,4), which is a new record of the form (k,m,k-m) ! Here is his splendid discovery:31138+20128+19538+8618=28238+27678+25578+112888th November 2006: Robert Gerbicz found 2 new solutions for (4,1,3), using his new program. His program is 100 times faster than Daniel J. Bernstein's !!!6th November 2006: Nuutti Kuosa sent a lot of new solutions for powers 7 and 8, but no record.5th November 2006: Sorry for the lack of update, but I was busy with the contest site I code and also on a Flash version of my peg solitaire game. I was also very lazy.4th November 2006: Jaroslaw Wroblewski found the following 1,3,7 multigrades:(7,4,4) 33704+32317+14977+9803=33450+32630+14664+10057(7,4,4) 76925+52473+50279+15187=74895+64419+27857+27693(7,4,4) 58711+42312+38285+9544=56170+51782+24427+16473(7,3,5) 1205011+744503+678161=1186971+921065+235693+187391+965552nd November 2006: Robert Gerbicz found a new solution to (4,1,3):1171120814=878656174+349185204+106161120425th October 2006: Robert Gerbicz sent me a faster program to compute (6,2,5), in other words, it may be able to boost our current distributed project !The source code is here: euler.c9th October 2006: Duncan Moore found several new results on 8th power:10568+1298+18=10178+8738+7108+2808+1708+8684698+3888+3148+28=4828+2748+2108+1498+3485648+1398+528+88=5408+4768+3648+2998+17489088+5308+4578+3498=8508+7918+6788+1258+4683rd October 2006: Jaroslaw Wroblewski found a 18th solution to (9,k,10-k):21529+9799+7529+5149=21019+17939+10219+8709+7509+112920th September 2006: I migrated my DNS from Gandi to 1and1. It's much cheaper and provides the same service.11th September 2006: Alexander Fischer improved the non-crossing knight tours of the 14x14 from 134 to 135, and 16x16 from 182 to 183.3rd August 2006: Jaroslaw Wroblewski collected solutions to 3rd and 4th powers:http://www.math.uni.wroc.pl/~jwr/eslp/tables.htm13th March 2006: Seiji Tomita discovered several new solution to (4,1,3):5826652964+2600523854+1866680004=589845921416706172714+6326719604+502378004=16791427294224955952840404+75924319813914+272397916926404=299998579386094and the Ramanujan-type identity:(2x2+36x-54)4+(2x2-36x-54)4+(4x2-108)4+(4x2+108)4+(3x2+81)4=(5x2+135)4His homepage is http://www3.alpha-net.ne.jp/users/fermat/index.html16th January 2006: Doomeva from AMDUsers team sent me several logos:11th January 2006: Tito Piezas posted a new conjecture (and kindly dedicated it to us):http://www.geocities.com/titus_piezas/Timeline1.htm4th January 2006: Jaroslaw Wroblewski built a list of 40 solutions to a4-b4=c4-d4=e4-f4.1st January 2006: Yasutoshi Kohmoto sent a nice equation for 2006:20066=38583643+19765003+243083=35905963+26622723-255123=35615353+27137053+267863And yes, it's the seventh birthday of our distributed project !Older results can be found hereKNOWN LOWER BOUNDSk\m1234567891011121314151622               332              43(RF)2              54(LP)3(BS)              67(LP)5(EB&GR)3(SR)             77(MD)6(JCM)5(RE)4(RE)            88(SIC)7(SIC)5(SIC)4(NK)            910(JW)8(JW)8(JW)6(RE)5(RE)           1012(JW)12(NK)11(JW)9(JW)7(JW)6(RE)          1115(JW)14(JW)11(NK)10(NK)9(NK)8(NK)7(NK)         1219(JW)17(JW)15(JW)15(JW)15(JW)11(JW)7(GC)         1321(JW)20(JW)18(JW)18(JW)15(JW)15(JCM)13(FY)9(GC)        1425(JW)21(JW)19(JW)18(JW)17(JW)16(JW)13(GC)12(JW)9(JW)       1528(JW)24(JW)23(JW)19(JW)2016(JW)14(JW)14(JW)13(JW)11(JW)      1649(JW)36(JW)36(JW)35(JW)35(JW)35(JW)27(SIC)22(GC)23(SIC)24(FY)12(TA)     1739(JW)4035(JW)33(JW)33(JW)30(GC)23(TA)24(GC)23(GC)20(DM)21(TA)18(GC)18(GC)14(GC)  1857(JW)57(JW)57(JW)44(FY)43(TA)34(TA)3536(TA)35(MLI)34(FY)29(GC)28(FY)29(FY)16(GC)15(GC) 1951(JW)525351(JW)43(GC)40(FY)41(FY)36(FY)33(GC)29(GC)3031(GC)27(GC)27(GC)21(GC)17(GC)2061(JW)6261(FY)60(FY)59(FY)53(TA)39(TA)4041(GC)35(FY)35(FY)35(FY)35(GC)35(FY)35(FY)26(GC)2175(FY)72(FY)67(TA)60(FY)57(TA)50(FY)5146(TA)41(GC)39(GC)37(GC)34(GC)31(DM)27(GC)25(TA)262295(TA)75(FY)7672(FY)7373(FY)59(TA)57(FY)54(FY)54(FY)52(TA)36(GC)3737(GC)36(GC)37(GC)23105(FY)91(FY)87(FY)86(FY)81(FY)72(FY)62(FY)6362(FY)53(GC)49(FY)49(GC)41(TA)36(GC)37(GC)33(GC)24124(FY)116(FY)109(FY)97(FY)85(TA)85(FY)71(FY)727369(GC)57(FY)5858(FY)55(GC)52(FY)5325137(FY)118(FY)104(FY)94(GC)89(GC)9081(GC)8280(GC)80(GC)76(GC)70(GC)717269(DM)67(GC)26155(FY)136(FY)119(FY)116(GC)111(FY)106(FY)99(FY)10081(GC)8275(TA)7670(TA)52(SMS&JW)535427163(FY)146(TA)132(FY)118(FY)119104(FC)99(FC)10087(GC)888963(GC)64656656(GC)28204(FY)147(FY)148(JCM)128(FY)129124(JCM)124(TA)124(FY)124(FY)99(FY)96(GC)97(JCM)98(GC)74(GC)73(GC)74(FY)29173(TA)168(FC)145(FY)146147142(FY)143134(FY)125(FY)120(FY)115(FC)102(GC)96(GC)89(GC)9084(FY)30191(FY)188(FY)189164(FY)139(FY)140141142135(FC)134(FC)135(GC)106(FY)10710810980(TA)31233(GC&JW)205(GC&JW)205(GC&JW)191(GC&JW)184(GC&JW)182(GC&JW)160(TA&JW)161162162(GC&JW)153(TA&JW)151(TA&JW)149(TA&JW)150143(TA&JW)127(TA&JW)32230(FY)214(FY)210(TA)210(FY)194(FY)195196184(FY)183(FY)183(FY)179(TA)178(TA)168(GC)169157(GC)158LOWEST NUMBER OF TERMSk234567891011121314151617m+n3445(LP,BS)6(SR)8(RE,MD,JCM)8(NK,SIC)10(RE,JW)12(RE,JW)14(NK)14(GC)17(GC)18(JW)21(JW)23(TA)28(GC)k181920212223242526272829303132m+n30(GC)33(GC)37(TA)40(TA,GC)44(GC)46(GC)51(GC)55(LL,GC)54(TA)63(TA)66(GC)69(TA)72(GC)77(GC)84(GC)AL: AlorilAN: Aleksi NiemeläBS: Bob ScherDA: David AltenDM: Douglas McNeilEB: Edward BrisseEB2: Eric BainvilleFC: Frank ClowesFY: Fumitaka YuraGC: Greg ChildersGR: Giovanni RestaJC: Joe CrumpJCM: Jean-Charles MeyrignacJMC: John Michael CrumpJML: Joe MacLeanJW: Jaroslaw WroblewskiKEK: Kjeld Elholm KristensenKO: Kevin O'HareLHA: Larry HaysLHU: Luke HuittLL: Laurent LucasLM: Luigi MorelliLP: Lander and ParkinMD: Mark DodrillML: Marcin LipinskiMW: Mac WangNH: Norman HoNK: Nuutti KuosaPG: Pascal GelebartRE: Randy EklRF: Roger FryeRS: Rizos SakellariouSIC: Scott I.ChaseSR: Subba-RaoTA: Torbjörn AlmTN: Tommy NolanLEGENDpower (k)number of left terms (m)number of right terms (n), unexplorednumber of right terms (n), known lower boundnumber of right terms (n), best lower bound currently foundnumber of right terms (n), best lower bound conjecturednumber of right terms (n), best lower bound provednumber of right terms (n) that doesn't need to be exploredVisitor numberVisitor since 1st April 2000 (project started 1st January 1999).[return to top]Valid HTML 4.0!© 1999-2005 Jean-Charles Meyrignac<euler@free.fr>
 

Includes

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software

download,

computation

records,

and

project

description

on

its

research

into

mathematical

problems.

http://euler.free.fr/

Computing Minimum Equal Sums of Like Power 2008 September

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Includes client software download, computation records, and project description on its research into mathematical problems.

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