The following table consists of the 1,413 primitive 4th power Ramanujan solutions that are less than 1.0E+28.
The format is:
I^4 + J^4 = K^4 + L^4 = Result.
Permission is granted to everyone to copy/use the list without restrictions as long as acknowledgement is iincluded that the original author is Bill Butler - website http://www.durangobill.com
Note: No solution has been found to the 3-way problem. (I^4 + J^4 = K^4 + L^4 = M^4 + N^4)
Count I J K L I^4 + J^4
1 133 134 59 158 6.3532E+008
2 157 227 7 239 3.2628E+009
3 256 257 193 292 8.6574E+009
4 298 497 271 502 6.8900E+010
5 359 514 103 542 8.6410E+010
6 503 558 222 631 1.6096E+011
7 653 1176 76 1203 2.0944E+012
8 997 1342 878 1381 4.2315E+012
9 1784 1997 1324 2189 2.6034E+013
10 2026 2141 1042 2461 3.7860E+013
11 2131 2524 248 2797 6.1206E+013
12 1797 2854 1034 2949 7.6774E+013
13 2345 2986 1577 3190 1.0974E+014
14 2338 3351 1623 3494 1.5597E+014
15 2767 3147 661 3537 1.5670E+014
16 3966 4397 2694 4883 6.2119E+014
17 1283 5048 604 5053 6.5206E+014
18 4288 4303 3364 4849 6.8091E+014
19 4840 5461 2027 6140 1.4381E+015
20 5093 5942 274 6619 1.9194E+015
21 5222 6057 498 6761 2.0896E+015
22 3070 6701 2707 6730 2.1051E+015
23 4661 7269 1259 7557 3.2639E+015
24 6336 7037 5181 7604 4.0638E+015
25 7432 7559 1657 8912 6.3157E+015
26 3391 9065 635 9109 6.8848E+015
27 6842 8409 4903 9018 7.1915E+015
28 5403 8972 1104 9253 7.3319E+015
29 6742 8531 5098 9043 7.3627E+015
30 4946 9097 1142 9289 7.4469E+015
31 4408 9197 173 9316 7.5321E+015
32 7234 8511 6262 8961 7.9856E+015
33 7528 9029 5452 9733 9.8576E+015
34 7054 9527 3401 10142 1.0714E+016
35 8103 9517 5277 10409 1.2515E+016
36 8332 9533 3779 10652 1.3078E+016
37 5960 11333 3644 11515 1.7758E+016
38 3550 12213 1525 12234 2.2407E+016
39 10203 10381 2903 12231 2.2450E+016
40 7809 12167 1149 12653 2.5633E+016
41 9153 12772 5121 13472 3.3628E+016
42 11022 12169 5526 13751 3.6688E+016
43 8171 14190 6470 14421 4.5002E+016
44 11379 13268 6496 14643 4.7756E+016
45 8427 14461 261 14861 4.8774E+016
46 8461 14723 581 15109 5.2113E+016
47 12743 13085 6101 15265 5.5684E+016
48 6485 15594 5675 15642 6.0902E+016
49 11291 14767 4441 15869 6.3805E+016
50 10411 15663 691 16377 7.1935E+016
51 11877 15188 7168 16293 7.3110E+016
52 13268 15091 8947 16628 8.2855E+016
53 13297 15566 9649 16886 8.9971E+016
54 6673 17236 529 17332 9.0239E+016
55 6049 17600 2207 17660 9.7290E+016
56 13869 16349 5981 18093 1.0844E+017
57 9609 18520 4912 18825 1.2617E+017
58 16213 17554 4058 20117 1.6405E+017
59 2541 21586 1098 21587 2.1716E+017
60 14539 21027 4091 22131 2.4017E+017
61 9738 24079 6502 24207 3.4516E+017
62 20201 20781 10191 24187 3.5302E+017
63 19447 21526 14327 23702 3.5774E+017
64 19218 25451 5653 27294 5.5599E+017
65 7217 27374 758 27407 5.6422E+017
66 23041 24041 17549 26867 6.1589E+017
67 4189 28058 2558 28061 6.2007E+017
68 22107 25355 15393 27785 6.5214E+017
69 24959 26511 12787 30411 8.8204E+017
70 24263 28308 9351 31472 9.8871E+017
71 21940 29617 10255 31544 1.0011E+018
72 25596 27661 5468 31731 1.0147E+018
73 23109 29812 6484 32187 1.0751E+018
74 5565 32237 4535 32241 1.0809E+018
75 26851 34107 7713 36977 1.8730E+018
76 29083 33614 27238 34651 1.9921E+018
77 13348 37721 167 37868 2.0563E+018
78 30348 35885 3080 39789 2.5065E+018
79 21676 38939 17701 39448 2.5198E+018
80 30713 36001 25489 38281 2.5696E+018
81 19304 39521 17887 39668 2.5784E+018
82 11888 40465 2513 40540 2.7011E+018
83 26479 39282 2438 41169 2.8727E+018
84 24858 40039 5322 41447 2.9518E+018
85 29297 38887 227 41699 3.0234E+018
86 20169 41968 3959 42516 3.2677E+018
87 28544 41591 11447 43676 3.6561E+018
88 25097 43007 1499 44203 3.8178E+018
89 34419 41324 15052 45453 4.3196E+018
90 18292 45883 10757 46136 4.5440E+018
91 25447 45471 12777 46481 4.6943E+018
92 41524 43847 26887 49792 6.6692E+018
93 42782 44337 1359 51826 7.2142E+018
94 35710 52881 31494 53935 9.4460E+018
95 36688 52837 15428 55589 9.6056E+018
96 28484 56089 3632 56999 1.0555E+019
97 40018 55947 33611 57702 1.2362E+019
98 50139 51176 41316 56603 1.3179E+019
99 48271 53742 45942 55247 1.3771E+019
100 33237 59777 28997 60369 1.3989E+019
101 17743 61478 5966 61583 1.4384E+019
102 38395 59634 31510 60987 1.4820E+019
103 26477 61892 17036 62317 1.5165E+019
104 38078 60763 29531 62206 1.5734E+019
105 46747 59693 40351 62047 1.7472E+019
106 46063 60033 23841 64369 1.7491E+019
107 45471 61528 27103 65196 1.8607E+019
108 55595 58918 6805 68174 2.1603E+019
109 46130 65521 33050 68303 2.2958E+019
110 57706 58841 43646 66407 2.3076E+019
111 56941 60328 45869 66308 2.3758E+019
112 52030 64803 822 70685 2.4964E+019
113 53112 64829 40876 69123 2.5621E+019
114 56767 62512 7612 71167 2.5655E+019
115 38599 70594 3698 72121 2.7055E+019
116 37143 71807 1661 73059 2.8490E+019
117 37404 72599 11884 73833 2.9737E+019
118 54212 68301 5728 74253 3.0400E+019
119 54044 68587 6464 74411 3.0660E+019
120 56837 68477 8207 75457 3.2423E+019
121 50747 71346 19134 75451 3.2543E+019
122 63161 64342 35582 74887 3.3053E+019
123 42313 74523 17697 76333 3.4049E+019
124 58593 71089 22813 78021 3.7326E+019
125 61966 69605 44315 76562 3.8217E+019
126 37631 79419 8427 80399 4.1788E+019
127 37593 80623 14493 81539 4.4248E+019
128 59728 75847 14983 82252 4.5821E+019
129 54520 78621 37996 81885 4.7043E+019
130 66269 74167 23359 83771 4.9544E+019
131 61889 80484 48524 84543 5.6631E+019
132 55073 85173 39393 87797 6.1826E+019
133 59678 84545 15322 89345 6.3776E+019
134 74941 76216 68989 80804 6.5284E+019
135 13397 90122 802 90133 6.5999E+019
136 54649 87548 37304 90041 6.7666E+019
137 69471 81622 37686 90017 6.7677E+019
138 43307 89841 27879 90829 6.8665E+019
139 45949 90937 20023 92333 7.2843E+019
140 58231 89236 2359 93032 7.4908E+019
141 55733 92213 37879 94543 8.1953E+019
142 29882 97489 17006 97681 9.1125E+019
143 31013 97982 17354 98203 9.3094E+019
144 84059 85498 82651 86774 1.0336E+020
145 60752 98427 1788 101819 1.0748E+020
146 72389 98049 47139 103543 1.1988E+020
147 57582 102451 13614 104909 1.2116E+020
148 68397 100292 4307 105324 1.2306E+020
149 83004 94529 57832 103809 1.2731E+020
150 78952 97907 5444 106931 1.3074E+020
151 76405 99978 27275 107478 1.3399E+020
152 81019 98879 17657 108499 1.3868E+020
153 83943 99904 47928 109543 1.4927E+020
154 54466 108867 10734 110531 1.4927E+020
155 74845 104534 4390 110813 1.5079E+020
156 54997 110448 26436 112021 1.5796E+020
157 81321 106696 15209 114732 1.7333E+020
158 72143 110834 64642 112561 1.7799E+020
159 76767 111838 29286 117473 1.9117E+020
160 61097 117205 27653 119225 2.0264E+020
161 98758 102441 74814 114839 2.0525E+020
162 83693 112199 49003 119183 2.0754E+020
163 61007 118668 35249 120468 2.1216E+020
164 87049 114176 74812 118327 2.2736E+020
165 72960 122579 12840 126253 2.5411E+020
166 62209 124402 46591 125714 2.5448E+020
167 104133 109213 39717 126659 2.5985E+020
168 102916 112363 44309 127916 2.7159E+020
169 66787 127037 20297 129377 2.8034E+020
170 108619 110758 73547 127034 2.8968E+020
171 111637 114613 34813 134413 3.2788E+020
172 100807 123497 59327 134111 3.3588E+020
173 49328 139505 3800 140047 3.8468E+020
174 112507 122664 55483 139356 3.8662E+020
175 105269 127578 91318 133557 3.8771E+020
176 72723 138631 66981 139361 3.9732E+020
177 117763 122332 99331 133636 4.1628E+020
178 37370 142993 18257 143150 4.2003E+020
179 99409 135504 8052 144401 4.3480E+020
180 91196 138379 82763 140432 4.3584E+020
181 72997 142871 66253 143647 4.4505E+020
182 73766 144541 72274 144733 4.6609E+020
183 101042 142251 4906 150549 5.1370E+020
184 119809 135502 9023 152662 5.4316E+020
185 99848 145627 91508 147941 5.4914E+020
186 75501 151421 23073 153689 5.5820E+020
187 129004 129777 14652 153871 5.6061E+020
188 79112 152393 23287 155068 5.7851E+020
189 125844 135829 113003 143844 5.9119E+020
190 129644 133383 78804 153863 5.9901E+020
191 92839 151394 73703 154522 5.9962E+020
192 30649 158736 6696 158791 6.3578E+020
193 56635 159544 28580 160133 6.5821E+020
194 85491 157582 77811 158642 6.7005E+020
195 79819 162613 8027 164923 7.3982E+020
196 113690 156939 54155 166314 7.7370E+020
197 41003 166806 5397 166958 7.7702E+020
198 121281 156580 31233 169040 8.1745E+020
199 125516 161405 7805 174484 9.2688E+020
200 136131 156241 29259 175033 9.3933E+020
201 131760 161951 126168 164705 9.8931E+020
202 33499 178509 18657 178559 1.0167E+021
203 145283 155762 35114 179261 1.0341E+021
204 91407 176524 42708 179471 1.0408E+021
205 142049 162527 58931 181819 1.1049E+021
206 127689 174574 72582 184823 1.1946E+021
207 148247 171266 50327 191218 1.3434E+021
208 153898 171481 50774 194087 1.4257E+021
209 148609 177440 117695 189412 1.4790E+021
210 31573 197949 5067 197981 1.5364E+021
211 166135 168254 48478 198665 1.5632E+021
212 151996 179143 77636 197689 1.5636E+021
213 93141 197378 39914 199701 1.5930E+021
214 125108 192459 46133 200388 1.6170E+021
215 36350 200581 6758 200635 1.6204E+021
216 161921 188610 55935 209954 1.9529E+021
217 82788 213689 43648 214791 2.1321E+021
218 88141 214793 59519 215989 2.1889E+021
219 153664 203349 116309 213672 2.2674E+021
220 67433 218289 36693 218741 2.2912E+021
221 47769 219256 23641 219372 2.3162E+021
222 112885 216868 68149 220240 2.3744E+021
223 127176 214519 25079 220848 2.3793E+021
224 118633 216119 33379 220837 2.3797E+021
225 130974 215011 6819 222058 2.4315E+021
226 183769 194937 99083 223341 2.5845E+021
227 138394 219121 88198 226063 2.6722E+021
228 44393 228825 22125 228901 2.7455E+021
229 171973 209302 37819 229862 2.7937E+021
230 121061 228784 79324 232357 2.9545E+021
231 163950 218423 92202 232585 2.9986E+021
232 177427 212576 6061 234676 3.0330E+021
233 109951 233212 81416 235201 3.1042E+021
234 191512 207139 190444 207971 3.1862E+021
235 179638 215545 75230 237241 3.1998E+021
236 152623 231462 41858 241647 3.4128E+021
237 198046 211123 22354 243661 3.5251E+021
238 132359 241564 95344 245447 3.7120E+021
239 118920 247067 52965 250192 3.9261E+021
240 134611 248034 64851 252974 4.1132E+021
241 122527 249751 53797 253163 4.1161E+021
242 131455 253172 112304 255295 4.4069E+021
243 138517 255532 112213 258616 4.6318E+021
244 88046 260311 32458 261143 4.6518E+021
245 214087 230457 72013 264501 4.9214E+021
246 196343 243690 164745 255718 5.0127E+021
247 52361 266116 36553 266192 5.0227E+021
248 217443 230099 72489 266063 5.0388E+021
249 42112 270853 14533 270892 5.3850E+021
250 214782 240557 193901 252474 5.4768E+021
251 203329 253814 49729 276598 5.8594E+021
252 230499 237317 129289 274953 5.9946E+021
253 186689 263323 143749 273503 6.0226E+021
254 218924 250683 128472 278011 6.2462E+021
255 151361 277724 95248 282751 6.4740E+021
256 67429 287178 20773 287394 6.8222E+021
257 201036 271067 10651 289584 7.0323E+021
258 247185 248792 197356 278865 7.5646E+021
259 222103 267769 140401 291151 7.5743E+021
260 243351 255520 204585 278524 7.7698E+021
261 192993 283604 145256 293409 7.8565E+021
262 221408 277049 152569 296732 8.2946E+021
263 242350 269959 193166 292985 8.7608E+021
264 241759 271673 215719 286079 8.8635E+021
265 206221 291524 21299 308272 9.0312E+021
266 226531 283546 35683 308822 9.0973E+021
267 237370 278741 181013 300350 9.2115E+021
268 249211 271132 227387 284896 9.2613E+021
269 243762 282241 88577 314754 9.8764E+021
270 228751 298497 40493 321429 1.0677E+022
271 238521 297565 36479 324405 1.1077E+022
272 206576 316137 23383 329652 1.1810E+022
273 180541 322821 128053 328563 1.1923E+022
274 222306 315223 161559 328426 1.2316E+022
275 182869 327183 30519 334883 1.2578E+022
276 264047 296668 1169 335084 1.2607E+022
277 268441 295116 166448 331047 1.2778E+022
278 220803 328619 136321 342081 1.4039E+022
279 183687 339587 63793 346533 1.4437E+022
280 240394 332259 155997 349582 1.5527E+022
281 270206 318437 133882 351653 1.5613E+022
282 183033 350254 146514 354041 1.6172E+022
283 253501 332463 117177 356533 1.6347E+022
284 149387 356663 130841 357787 1.6680E+022
285 289111 315957 217863 348197 1.6952E+022
286 135493 359575 43399 361355 1.7054E+022
287 251501 338310 177070 356307 1.7101E+022
288 191137 358090 143066 362975 1.7777E+022
289 184631 363179 152101 366407 1.8559E+022
290 204707 364050 156674 369885 1.9321E+022
291 288729 335248 235559 358416 1.9581E+022
292 284813 338918 33058 374989 1.9774E+022
293 301387 333384 94108 378507 2.0604E+022
294 157775 379674 96207 382090 2.1400E+022
295 281675 362111 69827 391385 2.3489E+022
296 241008 377969 110912 392079 2.3783E+022
297 323605 338231 238231 379915 2.4054E+022
298 265227 373213 168897 391681 2.4350E+022
299 317047 349162 35593 397498 2.4967E+022
300 221389 394911 100713 403931 2.6724E+022
301 251347 391475 224405 397403 2.7478E+022
302 332415 361208 159105 411208 2.9233E+022
303 340278 356585 176279 411270 2.9575E+022
304 248289 401168 17228 415137 2.9701E+022
305 81659 419762 31238 419909 3.1091E+022
306 300187 390315 15909 420715 3.1329E+022
307 239359 410253 19687 421653 3.1610E+022
308 219941 414008 34331 422012 3.1719E+022
309 314666 386259 202886 417453 3.2063E+022
310 327024 386989 57612 428947 3.3865E+022
311 355522 366409 212617 422806 3.4000E+022
312 315252 398693 293016 408229 3.5144E+022
313 101757 433912 33219 434236 3.5556E+022
314 287083 417688 139627 438136 3.7230E+022
315 319608 406397 185348 437187 3.7712E+022
316 325521 405511 122709 441637 3.8269E+022
317 327476 408945 126000 445007 3.9468E+022
318 224334 444263 72554 451239 4.1487E+022
319 156749 455536 17677 457124 4.3665E+022
320 381583 389242 279311 441718 4.4156E+022
321 318098 430987 54382 459893 4.4742E+022
322 344563 424780 93200 464563 4.6653E+022
323 305726 447339 120074 469461 4.8781E+022
324 246079 462034 113279 470666 4.9239E+022
325 214737 466387 133443 470783 4.9440E+022
326 289571 454187 66047 471841 4.9585E+022
327 373181 418014 144006 471677 4.9927E+022
328 335108 439847 292304 454681 5.0040E+022
329 378505 414987 357785 428763 5.0183E+022
330 201718 474839 162583 477058 5.2493E+022
331 345588 444311 108201 480032 5.3235E+022
332 106163 482944 70157 483172 5.4526E+022
333 175320 483131 166408 483525 5.5428E+022
334 349574 450737 77914 486833 5.6209E+022
335 405359 418394 176687 487906 5.7643E+022
336 148037 499968 123141 500468 6.2964E+022
337 277637 490336 131176 501893 6.3748E+022
338 225461 499133 61397 504221 6.4652E+022
339 180847 503469 118383 505171 6.5322E+022
340 396792 450695 348208 476025 6.6049E+022
341 365005 471849 340995 481607 6.7319E+022
342 266857 499784 2089 509644 6.7463E+022
343 360643 478157 127163 512389 6.9190E+022
344 175754 513625 59870 515353 7.0550E+022
345 349142 486287 31409 515794 7.0780E+022
346 360303 487022 142934 519249 7.3112E+022
347 304749 508048 177084 522029 7.5247E+022
348 418449 459689 120947 523491 7.5313E+022
349 378327 485288 338921 500508 7.5949E+022
350 305859 511160 46787 526800 7.7021E+022
351 434539 452420 196565 525152 7.7550E+022
352 370319 494186 1457 529234 7.8450E+022
353 376271 498473 149317 533957 8.1785E+022
354 112417 535349 12541 535609 8.2298E+022
355 364829 504474 111459 535658 8.2483E+022
356 436015 465994 180881 535490 8.3296E+022
357 435687 470878 119014 539943 8.5195E+022
358 113603 540164 61 540428 8.5300E+022
359 441137 466709 147971 539689 8.5314E+022
360 401364 496609 107487 542536 8.6773E+022
361 330352 524955 262811 536880 8.7853E+022
362 386419 511968 191688 547187 9.0999E+022
363 444748 481673 221129 548576 9.2953E+022
364 258176 547461 57669 554092 9.4271E+022
365 410170 515377 306002 547855 9.8855E+022
366 441873 498010 170790 560623 9.9634E+022
367 377271 531145 227697 558305 9.9848E+022
368 458668 491447 447344 500087 1.0259E+023
369 461939 493141 17201 568801 1.0467E+023
370 102653 569459 21103 569609 1.0527E+023
371 86299 570971 50131 571037 1.0634E+023
372 223828 569873 116143 572992 1.0798E+023
373 297888 565303 167836 574857 1.1000E+023
374 264821 569856 256212 570677 1.1037E+023
375 258641 571091 77059 576959 1.1085E+023
376 288534 567863 54647 577086 1.1092E+023
377 442111 522917 324341 565007 1.1298E+023
378 349171 564730 346622 565325 1.1657E+023
379 490250 500971 417515 548278 1.2075E+023
380 486366 516731 32517 597262 1.2725E+023
381 436647 549983 254171 593019 1.2785E+023
382 432496 558911 412801 567244 1.3257E+023
383 310631 593536 78937 604324 1.3342E+023
384 457813 557411 211511 610009 1.4047E+023
385 321186 602917 8539 614706 1.4278E+023
386 402007 585561 25557 615677 1.4369E+023
387 154637 625542 42099 626122 1.5369E+023
388 472371 570982 263859 623606 1.5608E+023
389 356793 613061 117009 629747 1.5746E+023
390 191905 630563 37945 631909 1.5945E+023
391 317810 622241 261985 627862 1.6011E+023
392 278128 628051 34468 634003 1.6157E+023
393 469124 580111 233969 631156 1.6169E+023
394 341849 623861 214349 635423 1.6514E+023
395 105709 638366 41918 638483 1.6619E+023
396 426507 604555 85993 638895 1.6667E+023
397 375404 619781 225188 637189 1.6742E+023
398 445397 599511 196179 639311 1.6853E+023
399 505829 567683 3119 641471 1.6932E+023
400 477241 586007 381101 620987 1.6980E+023
401 287284 636541 266819 638224 1.7099E+023
402 543128 544027 282836 640421 1.7461E+023
403 426592 616049 305713 640612 1.7715E+023
404 537338 554063 358894 633457 1.7761E+023
405 510316 579023 407356 625103 1.8022E+023
406 449517 611773 174243 651341 1.8091E+023
407 526953 573782 263106 651991 1.8550E+023
408 507984 589471 81249 657848 1.8733E+023
409 396619 636773 181171 658547 1.8916E+023
410 140290 662901 43893 663230 1.9349E+023
411 440117 631987 168301 665579 1.9705E+023
412 148239 680584 123396 680783 2.1503E+023
413 483295 635586 39414 683105 2.1775E+023
414 516186 623869 284803 681654 2.2248E+023
415 467327 651821 403283 670207 2.2821E+023
416 535674 629819 424494 674693 2.3969E+023
417 464957 662971 2449 699871 2.3992E+023
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