Computing Minimal Equal Sums Of High Like Powers


This page stores the status of the search on powers above 32.


High power database 12/05/2002


05- December 2002: Laurent Lucas sent 2 improvements.
27 November 2002:
Torbjörn improved 67 and 75 usings Jarek's congurences.
23 Novenber 2002:
Torbjörn found (91,1,12230) using Jarek's congurences.
14 November 2002:
49 slightly improved by Torbjörn. 15 November too.
13 November 2002:
Jaroslaw Wroblenski has made newcongurences for 49 and 98. Torbjörn improved 49.
12 November 2002:
68 improved by Greg, 37 slightly improved by Torbjörn.
10 November 2002:
The first 68-result from Greg using ResultLC with the first output!
9 November 2002:
Greg sent improvments on 73 and 85 (12*k+1)!
8 November 2002:
Torbjörn attacked 97, found (97,1,13221). 97 follows the 12*k+1 pattern. 97 down to (1,97,11362)
7 November 2002:
Greg improved 73 and 85, Torbjörn improved 85.
6 November 2002:
Torbjörn made 86 now below 10000, new results for 73 and 85 from Greg!
5 November 2002:
First try on 86.
4 November 2002:
(62,1,2140) found. Jarek sent new congurences. Greg improved 73 and 85!
3 November 2002:
Greg sent 62+63. All but 73 now below 4000 of the once big 5!
Greg sent more 62+63, both below 3000.
2 November 2002:
Greg sent improvments on 61 and 74.
1 November 2002:
Greg sent improvments on 61 and 74 using Jarek's congurences!
31 October 2002:
More from Greg and Torbjörn. 61 & 62 down again. 85 is now the first 5 digit power.
30 October 2002:
61 etc. almost blown to dust!
29 October 2002:
Jarek sent congurence for 61,62,63,71,74. Improvments on 61,62,62. Greg fixed 73 + 38.
27 October 2002:
Greg again! 37 below 400!!!
26 October 2002:
Greg improved 37 again! 37 is now almost below 400!!!
25 October 2002:
37 and 38 now below 500!
24 October 2002:
Jaroslaw Wroblenski has opened up a brand new road to the hard ones. 37 is now below 523!!! 38 is coming down too.
27 September 2002:
73, 85 and 97 improved.
20 September 2002:
61 improved again.
18 September 2002:
73 and 61 improved. 61 down to 100000, 73 to 150000.
16 September 2002:
73 and 61 improved. 73 below 200000. 61: terms above 16 down below 100000.
10 September 2002:
62, 73 and 74 improved again.
09 September 2002:
73 and 74 improved again.
04 September 2002:
Some more improvments by Torbjörn Alm
03 September 2002:
The new Large SumsBKZ makes it possible to attac the behemots.
62, 73 and 74 improved by Torbjörn Alm.
21 July 2002: Lucas Laurent sent improvments on 41, 42, 44, 45, and 47!
30 April 2003:
Lucas Laurent sent improvments on 43!
06 April 2002,:
Lucas Laurent has sent more results on 33, 38, 39!
29 March 2002:
Lucas Laurent has sent more results on 33, 36, 37
09 February 2002:
Lucas Laurent sent more results for 37!
21 January 2002:
Lucas Laurent sent more fantastic results for 37!!! Torbjörn Alm found (31,1,3821)
38 improved too.
19 January 2002:
Lucas Laurent sent very good results for 37. RHS side almost halved. Congratulations!
14 January 2002:
Improvments on 38
13 January 2002:
More improvments on 37
11 January
2002: The new SUMBKZ2 has improved 37 totally.
28 December 2001: A large number of results from Fumitaka Yura with improvments.
Congratulations!
31th August 2001: Greg Childers sent new results for 38 and for 61! First term dropped considerably.
28th August 2001:
Greg Childers sent improvments on 37
16th May 2001:
33 now below 300, all exponents up to 36 now below 400!
4th May 2001: 100 improved.
19th April 2001: 37, 61, and 74 improved
7th April 2001: 70 strongly improved.
3rd April 2001:
33 and 34 impoved.
31th March 2001:
68 strongly improved.
27th March 2001:
A large number of results from Laurent Lucas
21th March 2001:
A number of improvments by Torbjörn Alm
9th March 2001:
Laurent Lucas sent a number of solutions.
3rd March 2001:
Laurent Lucas sent a lot of new solutions (x,1,y).
2nd March 2001:
Laurent Lucas sent a lot of solutions on 61 and other exponents.
1st March 2001:
Laurent Lucas sent improved 37.
11th February 2001: 35 just above 400, 36 well below 400.
31th January 2001:
Counter added for visits.
29th January 2001: New home page for high powers now updated by Torbjörn Alm.
1st January 2001:
If you want to join the search on high powers (where you should have more success than low powers), join the internal mailing list here to send your results.
All best lower bounds are now less than 2,000 !
28th December 2000:
If you want to join the fun on this search, first download SumBKZ and check at Greg Childer's page how to use it. Download also Fumitaka Yura's ResultLC2, a tool to combine solutions to obtain better ones !
10th December 2000:
Creation of this page.

Jaroslaw Wroblenski's files with congurences are found here  


KNOWN LOWER BOUNDS
k\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
33 295
(TA)
218
(TA)
219 220 221 216
(TA)
207
(TA)
202
(TA)
199
(TA)
194
(TA)
167
(TA)
168 169 170 171 159
(LL)
34 318
(TA)
276
(TA)
268
(TA)
261
(TA)
254
(TA)
241
(TA)
225
(TA)
220
(TA)
221 213
(TA)
213
(TA)
207
(TA)
198
(TA)
199 193
(TA)
192
(TA)
35 395
(TA)
371
(TA)
342
(TA)
286
(TA)
287 285
(TA)
268
(TA)
269 258
(TA)
257
(TA)
245
(TA)
244
(TA)
244
(TA)
245 226
(TA)
227
36 377
(TA)
374
(TA)
375
(TA)
338
(TA)
338
(TA)
315
(TA)
303
(TA)
304
(TA)
269
(TA)
242
(TA)
243 244 245 238
(TA)
236
(TA)
237
(TA)
37 385
(GC&JW)
386 364
(GC&JW)
363
(GC&JW)
348
(GC&JW)
329
(GC&JW)
330 325
(GC&JW)
318
(GC&JW)
308
(TA&JW)
309 303
(GC&JW)
303
(GC&JW)
286
(GC&JW)
287 288
38 471
(GC&JW)
472 473 384
(GC&JW)
385 345
(GC&JW)
340
(TA&JW)
341 339
(GC&JW)
340 311
(GC&JW)
312 293
(GC&JW)
294 294
(GC&JW)
295
39 667
(TA)
525
(TA)
477
(TA)
478 408
(TA)
409 393
(TA)
394 359
(TA)
349
(TA)
350 331
(TA)
332 333 321
(TA)
322
40 745
(LL)
551
(TA)
499
(TA)
497
(TA)
459
(TA)
460 429
(TA)
430 431 391
(TA)
392 393 386
(TA)
387 386
(TA)
386
(TA)
41 610
(TA)
591
(TA)
574
(TA)
575 561
(TA)
438
(TA)
439 440 441 356
(GC)
357 356
(LL)
357 312
(TA)
309
(TA)
310
42 818
(TA)
605
(TA)
606 607
(TA)
582
(TA)
564
(TA)
438
(FY)
439 398
(TA)
399 400 401 402 402
(TA)
402
(TA)
400
(TA)
43 639
(TA)
595
(TA)
578
(TA)
536
(TA)
533
(TA)
504
(TA)
505 506 490
(TA)
479
(TA)
469
(TA)
456
(TA)
457 453
(TA)
439
(TA)
429
(TA)
44 809
(TA)
726
(TA)
675
(TA)
636
(TA)
601
(TA)
546
(TA)
547 529
(TA)
504
(TA)
491
(TA)
492 493 494 479
(TA)
480 475
(TA)
45 882
(TA)
877
(TA)
871
(TA)
747
(TA)
631
(TA)
632 626
(TA)
587
(TA)
541
(TA)
542 543 521
(TA)
522 521
(TA)
514
(TA)
494
(TA)
46 866
(GC)
761
(GC)
755
(GC)
664
(TA)
622
(TA)
575
(TA)
576 577 574
(TA)
534
(GC)
528
(GC)
528
(TA)
498
(GC)
499 500 488
(GC)
47 940
(TA)
906
(TA)
778
(TA)
779 757
(TA)
758 707
(TA)
682
(TA)
647
(TA)
648
(TA)
649 638
(TA)
629
(TA)
571
(TA)
572 557
(TA)
48 1077
(TA)
935
(TA)
936 925
(GC)
926 774
(TA)
775 776 777 733
(GC)
686
(TA)
687 667
(GC)
604
(TA)
605 606
49 939
(TA&JW)
940 908
(TA&JW)
824
(TA&JW)
816
(TA&JW)
817 797
(TA&JW)
750
(TA&JW)
751 752 753 670
(TA)
671 672 673 633
(TA&JW)
50 1164
(TA)
996
(TA)
945
(TA)
946 918
(TA)
899
(TA)
895
(TA)
896 891
(TA)
888
(TA)
876
(TA)
744
(TA)
739
(TA)
735
(TA)
719
(TA)
698
(TA)
51 1140
(TA)
1084
(TA)
1015
(TA)
1016 1013
(TA)
955
(TA)
894
(TA)
848
(TA)
824
(TA)
825 826 827 777
(TA)
765
(TA)
766
(TA)
713
(TA)
52 1826
(TA)
1350
(TA)
1288
(TA)
1194
(TA)
1122
(TA)
1123 1104
(TA)
1105 1079
(TA)
1080 1081 1071
(TA)
1072 1073 993
(TA)
994
53 1438
(TA)
1394
(TA)
1356
(TA)
1345
(TA)
1054
(TA)
1055 926
(TA)
927 924
(TA)
925 926 927 896
(TA)
897 898 895
(TA)
54 1772
(TA)
1582
(TA)
1496
(TA)
1468
(TA)
1253
(TA)
1225
(TA)
1185
(TA)
1186 1091
(TA)
1092 1067
(TA)
1068 1069 978
(TA)
956
(TA)
953
(TA)
55 1350
(TA)
1296
(TA)
1158
(TA)
1159 1160 1120
(TA)
1057
(TA)
1058 1011
(TA)
978
(TA)
979 980 981 982 955
(TA)
956
56 1772
(LL)
1497
(TA)
1478
(TA)
1437
(TA)
1394
(TA)
1389
(TA)
1350
(TA)
1283
(TA)
1230
(TA)
1231 1232 1051
(TA)
1052 1053 1054 1051
(TA)
57 2501
(FY)
1908
(TA)
1708
(TA)
1658
(TA)
1624
(TA)
1461
(TA)
1439
(TA)
1400
(TA)
1365
(TA)
1305
(TA)
1232
(TA)
1233 1234 1231
(TA)
1200
(TA)
1201
58 2071
(TA)
1911
(TA)
1909
(TA)
1794
(TA)
1673
(TA)
1615
(TA)
1499
(TA)
1319
(TA)
1317
(TA)
1318 1319 1320 1312
(TA)
1209
(TA)
1210 1211
59 2223
(FY)
2016
(TA)
2007
(TA)
1858
(TA)
1391
(TA)
1392 1393 1394 1395 1396 1397 1398 1384
(TA)
1385 1344
(TA)
1345
60 2703
(LL)
2256
(TA)
2212
(TA)
2164
(TA)
1937
(TA)
1938 1764
(TA)
1765 1766 1767 1499
(TA)
1500 1501 1502 1444
(TA)
1445
61 1818
(GC&JW)
1783
(GC&JW)
1721
(GC&JW)
1718
(GC&JW)
1714
(GC&JW)
1659
(GC&JW)
1660 1661 1662 1534
(GC&JW)
1535 1536 1517
(GC&JW)
1518 1519 1496
(GC&JW)
62 2140
(TA&JW)
2141 2142 1967
(TA&JW)
1968 1969 1970 1971 1972 1788
(TA&JW)
1786
(TA&JW)
1632
(TA&JW)
1633 1634 1635 1636
63 2819
(GC&JW)
2659
(GC&JW)
2546
(GC&JW)
2205
(GC&JW)
2206 2207 2208 2209 2202
(GC&JW)
2190
(GC)
2191 2192 2190
(GC&JW)
2180
(GC&JW)
2020
(GC)
2021
64 2738
(TA)
2739 2670
(TA)
2611
(TA)
2612 2613 2614 2580
(TA)
1938
(TA)
1939 1940 1941 1896
(TA)
1812
(TA)
1813 1814
65 3392
(TA)
2810
(TA)
2465
(TA)
2250
(TA)
2232
(TA)
2126
(TA)
1947
(TA)
1948 1777
(TA)
1778 1779 1780 1781 1722
(TA)
1723 1724
66 5662
(LL)
2620
(TA)
2563
(TA)
2456
(TA)
2420
(TA)
2421 2359
(TA)
2028
(TA)
2029 2030 2031 2032 1955
(TA)
1956 1957 1958
67 4079
(TA&JW)
3609
(TA)
3495
(TA)
3479
(TA)
2841
(TA)
2518
(TA)
2519 2520 2521 2448
(TA)
2449 2028
(TA)
2029 2030 2029
(TA)
2030
68 4394
(GC&JW)
3520
(GC&JW)
2587
(GC&JW)
2588 2589 2590 2575
(GC&JW)
2553
(GC&JW)
2554 2399
(TA)
2400 2383
(TA)
2345
(GC&JW)
2319
(GC&JW)
2189
(TA)
2190
69 5292
(LL)
3436
(TA)
3095
(TA)
3019
(TA)
2922
(TA)
2869
(TA)
2870 2871 2843
(TA)
2844 2785
(TA)
2770
(TA)
2721
(TA)
2722 2633
(TA)
2634
70 3148
(TA)
3081
(TA)
2953
(TA)
2935
(TA)
2861
(TA)
2846
(TA)
2784
(TA)
2785 2786 2510
(TA)
2428
(TA)
2429 2430 2431 2432 2242
(TA)
71 4832
(LL)
3536
(TA)
3537 3432
(TA)
3381
(TA)
3382 3156
(TA)
2930
(TA)
2834
(TA)
2835 2836 2837 2838 2637
(TA)
2638 2639
72 3690
(TA)
3691 3520
(TA)
3427
(TA)
3311
(TA)
2956
(TA)
2957 2680
(TA)
2681 2682 2683 2684 2685 2686 2677
(TA)
2583
(TA)
73 3555
(GC&JW)
3532
(GC&JW)
3506
(GC&JW)
3507 3408
(GC&JW)
3409 3410 3411 3412 3413 3414 3378
(GC&JW)
3379 3380 3381 3382
74 3928
(GC&JW)
3667
(GC&JW)
3668 3669 3670 3671 3484
(GC&JW)
3485 3421
(GC&JW)
3323
(GC&JW)
3324 3325 3326 3327 3328 3235
(GC&JW)
75 8160
(TA&JW)
8161 6414
(TA)
6415 6416 6266
(TA)
6267 6268 6269 6233
(TA)
6164
(TA)
5997
(TA)
5998 5877
(TA)
5878 5879
76 6780
(LL)
5319
(TA)
5254
(TA)
4712
(TA)
3823
(TA)
3824 3825 3826 3827 3828 3740
(TA)
3741 3666
(TA)
3667 3482
(TA)
3483
77 5177
(FY)
4797
(TA)
4056
(TA)
4057 3631
(TA)
3496
(TA)
3450
(TA)
3440
(TA)
3397
(TA)
3334
(TA)
3320
(TA)
3276
(TA)
3203
(TA)
3204 3194
(TA)
3195
78 5463
(TA)
5032
(TA)
4766
(TA)
4424
(TA)
4365
(TA)
4366 4367 3803
(TA)
3804 3505
(TA)
3506 3507 3508 3509 3510 3511
79 5685
(TA)
4950
(TA)
4951 4765
(TA)
4688
(TA)
4689 4429
(TA)
4430 4420
(TA)
4182
(TA)
4183 4129
(TA)
3879
(TA)
3880 3881 3680
(TA)
80 7651
(LL)
5655
(TA)
4611
(TA)
4612 4613 4614 4615 4616 4378
(TA)
4318
(TA)
4319 4148
(TA)
3944
(TA)
3903
(TA)
3827
(TA)
3828
81 7084
(LL)
6652
(TA)
6653 6562
(TA)
6563 4634
(TA)
4635 4636 4637 4638 4639 4640 3970
(TA)
3890
(TA)
3891 3715
(TA)
82 9665
(LL)
8737
(TA)
8337
(TA)
8010
(TA)
7373
(TA)
7333
(TA)
7319
(TA)
6204
(LL)
4708
(TA)
4709 4710 4711 4712 4713 4714 4715
83 7894
(LL)
6186
(TA)
5736
(TA)
5061
(TA)
5062 5063 5007
(TA)
4834
(TA)
4835 4836 4837 4838 4839 4840 4841 4842
84 7496
(LL)
6113
(TA)
6026
(TA)
5738
(TA)
5667
(TA)
5553
(TA)
5195
(TA)
5196 5197 5116
(TA)
4567
(TA)
4568 4569 4570 4571 4311
(TA)
85 5893
(GC&JW)
5573
(GC&JW)
5574 5575 5206
(TA&JW)
5207 5208 5209 5210 5211 5212 5191
(TA&JW)
5192 5193 5194 5195
(TA&JW)
86 9295
(TA&JW)
9296 9297 9298 9299 9300 9301 9302 9303 9261
(TA&JW)
8924
(TA&JW)
8925 8926 8927 8838
(TA&JW)
8839
87 9411
(LL)
6487
(TA)
6488 6080
(TA)
6081 5565
(TA)
5566 5567 5568 5569 5570 5506
(TA)
5507 5508 5509 5510
88 12874
(LL)
8923
(TA)
8084
(TA)
6859
(TA)
6630
(TA)
6352
(TA)
6353 6080
(TA)
6000
(TA)
5895
(TA)
5761
(TA)
5762 5763 5764 5558
(TA)
5559
89 11431
(LL)
10709
(TA)
9145
(TA)
8893
(TA)
7896
(TA)
5671
(TA)
5672 5424
(TA)
5425 5426 5427 5428 5429 5430 5431 5432
90 11017
(LL)
9153
(TA)
8288
(TA)
7918
(TA)
7919 7854
(TA)
7780
(TA)
7637
(TA)
7638 6697
(TA)
6698 6171
(TA)
6172 6173 6174 6175
91 12230
(TA&JW)
11084
(TA)
9722
(TA)
9310
(TA)
9311 7826
(TA)
7827 7828 7829 7830 7831 7118
(TA)
7097
(TA)
6857
(TA)
6858 6721
(TA)
92 9922
(LL)
9923 9924 9925 8489
(TA)
8306
(TA)
8239
(TA)
8166
(TA)
7727
(TA)
7728 7729 7730 7731 6602
(TA)
6603 6604
93 14590
(LL)
9440
(TA)
8714
(TA)
8391
(TA)
8241
(TA)
8242 8243 8096
(TA)
8097 7425
(TA)
7426 6802
(TA)
6803 6804 6805 6672
(TA)
94 15670
(LL)
12383
(TA)
9542
(TA)
9142
(TA)
8988
(TA)
8820
(TA)
8642
(TA)
8374
(TA)
8375 8093
(TA)
7573
(TA)
7574 7139
(TA)
7140 7141 7142
95 12940
(LL)
10469
(TA)
10059
(TA)
9979
(TA)
9980 9889
(TA)
8471
(TA)
8472 7798
(TA)
7799 7800 7801 7802 7803 7736
(TA)
7737
96 18670
(LL)
13620
(GC)
10573
(TA)
10574 9193
(TA)
9194 9195 9196 8873
(TA)
8874 8875 8876 8676
(TA)
8677 8678 8441
(TA)
97 11362
(TA&JW)
11363 11364 11015
(TA&JW)
11016 11017 11018 11019 10506
(TA&JW)
10507 10508 10509 10510 10511 10512 10513
98 19845
(LL)
13529
(FY)
13135
(TA)
11898
(TA)
11899 11772
(TA)
10305
(TA)
10306 10307 9641
(TA)
9642 9643 9644 9645 9646 9647
99 30611
(LL)
12527
(TA)
12528 12253
(TA)
10404 9801
(LL)
9625
(TA)
9626 9627 9628 9629 9264
(TA)
9265 9266 8717
(TA)
8718
100 14031
(TA)
12217
(GC)
12218 12124
(TA)
12025
(TA)
11937
(TA)
11938 11780
(TA)
11290
(GC)
11291 11292 11130
(GC)
11131 11132 11133 11134


LOWEST NUMBER OF TERMS
k 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
m+n 88
(LL)
101
(TA)
106
(TA)
107
(TA)
111
(LL)
117
(LL)
116
(TA)
140
(TA)
146
(TA)
148
(TA)
165
(LL)
161
(LL)
179
(LL)
196
(TA)
211
(LL,TA)
204
(GC)
218
(TA)
k 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
m+n 232
(TA)
243
(TA)
269
(TA)
279
(TA)
280
(TA)
295
(TA)
322
(TA)
317
(GC)
348
(TA)
357
(TA)
339
(LL)
362
(TA)
363
(LL)
402
(TA)
434
(TA)
460
(TA)
467
(TA)
k 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
m+n 481
(TA)
512
(GC&JW)
514
(TA)
607
(GC)
610
(GC)
684
(LL)
570
(GC)
680
(GC)
636
(TA)
703
(TA)
754
(TA)
770
(GC)
834
(TA)
905
(LL)
886
(TA)
905
(GC)
985
(LL)
k 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
m+n 983
(TA)
1048
(GC)
1048
(GC)
1074
(LL)
1132
(TA)
1194
(TA)
1266
(LL)
1229
(TA)
1382
(LL)
1339
(LL)
1489
(GC)
1673
(TA)
1412
(GC)
1453
(GC)
1522
(GC)
1621
(GC)
1654
(GC)
LEGEND

power (k)
number of left terms (m)
number of right terms (n), unexplored
number of right terms (n), known lower bound
number of right terms (n), best lower bound currently found
number of right terms (n), best lower bound conjectured
number of right terms (n), best lower bound proved
number of right terms (n) that doesn't need to be explored

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© 2001 Torbjörn Alm <torbjorn.alm@swipnet.se>