Celočíselné Diofantové rovnice
Rovnica je lineárna Diofantova rovnica s kladnými koeficientami
Počet nájdených riešení je príliš veľký - zobrazujem prvých 500.
x1 = 1 y1 = 3295 x2 = 4 y2 = 3293
x3 = 7 y3 = 3291
x4 = 10 y4 = 3289
x5 = 13 y5 = 3287
x6 = 16 y6 = 3285
x7 = 19 y7 = 3283
x8 = 22 y8 = 3281
x9 = 25 y9 = 3279
x10 = 28 y10 = 3277
x11 = 31 y11 = 3275
x12 = 34 y12 = 3273
x13 = 37 y13 = 3271
x14 = 40 y14 = 3269
x15 = 43 y15 = 3267
x16 = 46 y16 = 3265
x17 = 49 y17 = 3263
x18 = 52 y18 = 3261
x19 = 55 y19 = 3259
x20 = 58 y20 = 3257
x21 = 61 y21 = 3255
x22 = 64 y22 = 3253
x23 = 67 y23 = 3251
x24 = 70 y24 = 3249
x25 = 73 y25 = 3247
x26 = 76 y26 = 3245
x27 = 79 y27 = 3243
x28 = 82 y28 = 3241
x29 = 85 y29 = 3239
x30 = 88 y30 = 3237
x31 = 91 y31 = 3235
x32 = 94 y32 = 3233
x33 = 97 y33 = 3231
x34 = 100 y34 = 3229
x35 = 103 y35 = 3227
x36 = 106 y36 = 3225
x37 = 109 y37 = 3223
x38 = 112 y38 = 3221
x39 = 115 y39 = 3219
x40 = 118 y40 = 3217
x41 = 121 y41 = 3215
x42 = 124 y42 = 3213
x43 = 127 y43 = 3211
x44 = 130 y44 = 3209
x45 = 133 y45 = 3207
x46 = 136 y46 = 3205
x47 = 139 y47 = 3203
x48 = 142 y48 = 3201
x49 = 145 y49 = 3199
x50 = 148 y50 = 3197
x51 = 151 y51 = 3195
x52 = 154 y52 = 3193
x53 = 157 y53 = 3191
x54 = 160 y54 = 3189
x55 = 163 y55 = 3187
x56 = 166 y56 = 3185
x57 = 169 y57 = 3183
x58 = 172 y58 = 3181
x59 = 175 y59 = 3179
x60 = 178 y60 = 3177
x61 = 181 y61 = 3175
x62 = 184 y62 = 3173
x63 = 187 y63 = 3171
x64 = 190 y64 = 3169
x65 = 193 y65 = 3167
x66 = 196 y66 = 3165
x67 = 199 y67 = 3163
x68 = 202 y68 = 3161
x69 = 205 y69 = 3159
x70 = 208 y70 = 3157
x71 = 211 y71 = 3155
x72 = 214 y72 = 3153
x73 = 217 y73 = 3151
x74 = 220 y74 = 3149
x75 = 223 y75 = 3147
x76 = 226 y76 = 3145
x77 = 229 y77 = 3143
x78 = 232 y78 = 3141
x79 = 235 y79 = 3139
x80 = 238 y80 = 3137
x81 = 241 y81 = 3135
x82 = 244 y82 = 3133
x83 = 247 y83 = 3131
x84 = 250 y84 = 3129
x85 = 253 y85 = 3127
x86 = 256 y86 = 3125
x87 = 259 y87 = 3123
x88 = 262 y88 = 3121
x89 = 265 y89 = 3119
x90 = 268 y90 = 3117
x91 = 271 y91 = 3115
x92 = 274 y92 = 3113
x93 = 277 y93 = 3111
x94 = 280 y94 = 3109
x95 = 283 y95 = 3107
x96 = 286 y96 = 3105
x97 = 289 y97 = 3103
x98 = 292 y98 = 3101
x99 = 295 y99 = 3099
x100 = 298 y100 = 3097
x101 = 301 y101 = 3095
x102 = 304 y102 = 3093
x103 = 307 y103 = 3091
x104 = 310 y104 = 3089
x105 = 313 y105 = 3087
x106 = 316 y106 = 3085
x107 = 319 y107 = 3083
x108 = 322 y108 = 3081
x109 = 325 y109 = 3079
x110 = 328 y110 = 3077
x111 = 331 y111 = 3075
x112 = 334 y112 = 3073
x113 = 337 y113 = 3071
x114 = 340 y114 = 3069
x115 = 343 y115 = 3067
x116 = 346 y116 = 3065
x117 = 349 y117 = 3063
x118 = 352 y118 = 3061
x119 = 355 y119 = 3059
x120 = 358 y120 = 3057
x121 = 361 y121 = 3055
x122 = 364 y122 = 3053
x123 = 367 y123 = 3051
x124 = 370 y124 = 3049
x125 = 373 y125 = 3047
x126 = 376 y126 = 3045
x127 = 379 y127 = 3043
x128 = 382 y128 = 3041
x129 = 385 y129 = 3039
x130 = 388 y130 = 3037
x131 = 391 y131 = 3035
x132 = 394 y132 = 3033
x133 = 397 y133 = 3031
x134 = 400 y134 = 3029
x135 = 403 y135 = 3027
x136 = 406 y136 = 3025
x137 = 409 y137 = 3023
x138 = 412 y138 = 3021
x139 = 415 y139 = 3019
x140 = 418 y140 = 3017
x141 = 421 y141 = 3015
x142 = 424 y142 = 3013
x143 = 427 y143 = 3011
x144 = 430 y144 = 3009
x145 = 433 y145 = 3007
x146 = 436 y146 = 3005
x147 = 439 y147 = 3003
x148 = 442 y148 = 3001
x149 = 445 y149 = 2999
x150 = 448 y150 = 2997
x151 = 451 y151 = 2995
x152 = 454 y152 = 2993
x153 = 457 y153 = 2991
x154 = 460 y154 = 2989
x155 = 463 y155 = 2987
x156 = 466 y156 = 2985
x157 = 469 y157 = 2983
x158 = 472 y158 = 2981
x159 = 475 y159 = 2979
x160 = 478 y160 = 2977
x161 = 481 y161 = 2975
x162 = 484 y162 = 2973
x163 = 487 y163 = 2971
x164 = 490 y164 = 2969
x165 = 493 y165 = 2967
x166 = 496 y166 = 2965
x167 = 499 y167 = 2963
x168 = 502 y168 = 2961
x169 = 505 y169 = 2959
x170 = 508 y170 = 2957
x171 = 511 y171 = 2955
x172 = 514 y172 = 2953
x173 = 517 y173 = 2951
x174 = 520 y174 = 2949
x175 = 523 y175 = 2947
x176 = 526 y176 = 2945
x177 = 529 y177 = 2943
x178 = 532 y178 = 2941
x179 = 535 y179 = 2939
x180 = 538 y180 = 2937
x181 = 541 y181 = 2935
x182 = 544 y182 = 2933
x183 = 547 y183 = 2931
x184 = 550 y184 = 2929
x185 = 553 y185 = 2927
x186 = 556 y186 = 2925
x187 = 559 y187 = 2923
x188 = 562 y188 = 2921
x189 = 565 y189 = 2919
x190 = 568 y190 = 2917
x191 = 571 y191 = 2915
x192 = 574 y192 = 2913
x193 = 577 y193 = 2911
x194 = 580 y194 = 2909
x195 = 583 y195 = 2907
x196 = 586 y196 = 2905
x197 = 589 y197 = 2903
x198 = 592 y198 = 2901
x199 = 595 y199 = 2899
x200 = 598 y200 = 2897
x201 = 601 y201 = 2895
x202 = 604 y202 = 2893
x203 = 607 y203 = 2891
x204 = 610 y204 = 2889
x205 = 613 y205 = 2887
x206 = 616 y206 = 2885
x207 = 619 y207 = 2883
x208 = 622 y208 = 2881
x209 = 625 y209 = 2879
x210 = 628 y210 = 2877
x211 = 631 y211 = 2875
x212 = 634 y212 = 2873
x213 = 637 y213 = 2871
x214 = 640 y214 = 2869
x215 = 643 y215 = 2867
x216 = 646 y216 = 2865
x217 = 649 y217 = 2863
x218 = 652 y218 = 2861
x219 = 655 y219 = 2859
x220 = 658 y220 = 2857
x221 = 661 y221 = 2855
x222 = 664 y222 = 2853
x223 = 667 y223 = 2851
x224 = 670 y224 = 2849
x225 = 673 y225 = 2847
x226 = 676 y226 = 2845
x227 = 679 y227 = 2843
x228 = 682 y228 = 2841
x229 = 685 y229 = 2839
x230 = 688 y230 = 2837
x231 = 691 y231 = 2835
x232 = 694 y232 = 2833
x233 = 697 y233 = 2831
x234 = 700 y234 = 2829
x235 = 703 y235 = 2827
x236 = 706 y236 = 2825
x237 = 709 y237 = 2823
x238 = 712 y238 = 2821
x239 = 715 y239 = 2819
x240 = 718 y240 = 2817
x241 = 721 y241 = 2815
x242 = 724 y242 = 2813
x243 = 727 y243 = 2811
x244 = 730 y244 = 2809
x245 = 733 y245 = 2807
x246 = 736 y246 = 2805
x247 = 739 y247 = 2803
x248 = 742 y248 = 2801
x249 = 745 y249 = 2799
x250 = 748 y250 = 2797
x251 = 751 y251 = 2795
x252 = 754 y252 = 2793
x253 = 757 y253 = 2791
x254 = 760 y254 = 2789
x255 = 763 y255 = 2787
x256 = 766 y256 = 2785
x257 = 769 y257 = 2783
x258 = 772 y258 = 2781
x259 = 775 y259 = 2779
x260 = 778 y260 = 2777
x261 = 781 y261 = 2775
x262 = 784 y262 = 2773
x263 = 787 y263 = 2771
x264 = 790 y264 = 2769
x265 = 793 y265 = 2767
x266 = 796 y266 = 2765
x267 = 799 y267 = 2763
x268 = 802 y268 = 2761
x269 = 805 y269 = 2759
x270 = 808 y270 = 2757
x271 = 811 y271 = 2755
x272 = 814 y272 = 2753
x273 = 817 y273 = 2751
x274 = 820 y274 = 2749
x275 = 823 y275 = 2747
x276 = 826 y276 = 2745
x277 = 829 y277 = 2743
x278 = 832 y278 = 2741
x279 = 835 y279 = 2739
x280 = 838 y280 = 2737
x281 = 841 y281 = 2735
x282 = 844 y282 = 2733
x283 = 847 y283 = 2731
x284 = 850 y284 = 2729
x285 = 853 y285 = 2727
x286 = 856 y286 = 2725
x287 = 859 y287 = 2723
x288 = 862 y288 = 2721
x289 = 865 y289 = 2719
x290 = 868 y290 = 2717
x291 = 871 y291 = 2715
x292 = 874 y292 = 2713
x293 = 877 y293 = 2711
x294 = 880 y294 = 2709
x295 = 883 y295 = 2707
x296 = 886 y296 = 2705
x297 = 889 y297 = 2703
x298 = 892 y298 = 2701
x299 = 895 y299 = 2699
x300 = 898 y300 = 2697
x301 = 901 y301 = 2695
x302 = 904 y302 = 2693
x303 = 907 y303 = 2691
x304 = 910 y304 = 2689
x305 = 913 y305 = 2687
x306 = 916 y306 = 2685
x307 = 919 y307 = 2683
x308 = 922 y308 = 2681
x309 = 925 y309 = 2679
x310 = 928 y310 = 2677
x311 = 931 y311 = 2675
x312 = 934 y312 = 2673
x313 = 937 y313 = 2671
x314 = 940 y314 = 2669
x315 = 943 y315 = 2667
x316 = 946 y316 = 2665
x317 = 949 y317 = 2663
x318 = 952 y318 = 2661
x319 = 955 y319 = 2659
x320 = 958 y320 = 2657
x321 = 961 y321 = 2655
x322 = 964 y322 = 2653
x323 = 967 y323 = 2651
x324 = 970 y324 = 2649
x325 = 973 y325 = 2647
x326 = 976 y326 = 2645
x327 = 979 y327 = 2643
x328 = 982 y328 = 2641
x329 = 985 y329 = 2639
x330 = 988 y330 = 2637
x331 = 991 y331 = 2635
x332 = 994 y332 = 2633
x333 = 997 y333 = 2631
x334 = 1000 y334 = 2629
x335 = 1003 y335 = 2627
x336 = 1006 y336 = 2625
x337 = 1009 y337 = 2623
x338 = 1012 y338 = 2621
x339 = 1015 y339 = 2619
x340 = 1018 y340 = 2617
x341 = 1021 y341 = 2615
x342 = 1024 y342 = 2613
x343 = 1027 y343 = 2611
x344 = 1030 y344 = 2609
x345 = 1033 y345 = 2607
x346 = 1036 y346 = 2605
x347 = 1039 y347 = 2603
x348 = 1042 y348 = 2601
x349 = 1045 y349 = 2599
x350 = 1048 y350 = 2597
x351 = 1051 y351 = 2595
x352 = 1054 y352 = 2593
x353 = 1057 y353 = 2591
x354 = 1060 y354 = 2589
x355 = 1063 y355 = 2587
x356 = 1066 y356 = 2585
x357 = 1069 y357 = 2583
x358 = 1072 y358 = 2581
x359 = 1075 y359 = 2579
x360 = 1078 y360 = 2577
x361 = 1081 y361 = 2575
x362 = 1084 y362 = 2573
x363 = 1087 y363 = 2571
x364 = 1090 y364 = 2569
x365 = 1093 y365 = 2567
x366 = 1096 y366 = 2565
x367 = 1099 y367 = 2563
x368 = 1102 y368 = 2561
x369 = 1105 y369 = 2559
x370 = 1108 y370 = 2557
x371 = 1111 y371 = 2555
x372 = 1114 y372 = 2553
x373 = 1117 y373 = 2551
x374 = 1120 y374 = 2549
x375 = 1123 y375 = 2547
x376 = 1126 y376 = 2545
x377 = 1129 y377 = 2543
x378 = 1132 y378 = 2541
x379 = 1135 y379 = 2539
x380 = 1138 y380 = 2537
x381 = 1141 y381 = 2535
x382 = 1144 y382 = 2533
x383 = 1147 y383 = 2531
x384 = 1150 y384 = 2529
x385 = 1153 y385 = 2527
x386 = 1156 y386 = 2525
x387 = 1159 y387 = 2523
x388 = 1162 y388 = 2521
x389 = 1165 y389 = 2519
x390 = 1168 y390 = 2517
x391 = 1171 y391 = 2515
x392 = 1174 y392 = 2513
x393 = 1177 y393 = 2511
x394 = 1180 y394 = 2509
x395 = 1183 y395 = 2507
x396 = 1186 y396 = 2505
x397 = 1189 y397 = 2503
x398 = 1192 y398 = 2501
x399 = 1195 y399 = 2499
x400 = 1198 y400 = 2497
x401 = 1201 y401 = 2495
x402 = 1204 y402 = 2493
x403 = 1207 y403 = 2491
x404 = 1210 y404 = 2489
x405 = 1213 y405 = 2487
x406 = 1216 y406 = 2485
x407 = 1219 y407 = 2483
x408 = 1222 y408 = 2481
x409 = 1225 y409 = 2479
x410 = 1228 y410 = 2477
x411 = 1231 y411 = 2475
x412 = 1234 y412 = 2473
x413 = 1237 y413 = 2471
x414 = 1240 y414 = 2469
x415 = 1243 y415 = 2467
x416 = 1246 y416 = 2465
x417 = 1249 y417 = 2463
x418 = 1252 y418 = 2461
x419 = 1255 y419 = 2459
x420 = 1258 y420 = 2457
x421 = 1261 y421 = 2455
x422 = 1264 y422 = 2453
x423 = 1267 y423 = 2451
x424 = 1270 y424 = 2449
x425 = 1273 y425 = 2447
x426 = 1276 y426 = 2445
x427 = 1279 y427 = 2443
x428 = 1282 y428 = 2441
x429 = 1285 y429 = 2439
x430 = 1288 y430 = 2437
x431 = 1291 y431 = 2435
x432 = 1294 y432 = 2433
x433 = 1297 y433 = 2431
x434 = 1300 y434 = 2429
x435 = 1303 y435 = 2427
x436 = 1306 y436 = 2425
x437 = 1309 y437 = 2423
x438 = 1312 y438 = 2421
x439 = 1315 y439 = 2419
x440 = 1318 y440 = 2417
x441 = 1321 y441 = 2415
x442 = 1324 y442 = 2413
x443 = 1327 y443 = 2411
x444 = 1330 y444 = 2409
x445 = 1333 y445 = 2407
x446 = 1336 y446 = 2405
x447 = 1339 y447 = 2403
x448 = 1342 y448 = 2401
x449 = 1345 y449 = 2399
x450 = 1348 y450 = 2397
x451 = 1351 y451 = 2395
x452 = 1354 y452 = 2393
x453 = 1357 y453 = 2391
x454 = 1360 y454 = 2389
x455 = 1363 y455 = 2387
x456 = 1366 y456 = 2385
x457 = 1369 y457 = 2383
x458 = 1372 y458 = 2381
x459 = 1375 y459 = 2379
x460 = 1378 y460 = 2377
x461 = 1381 y461 = 2375
x462 = 1384 y462 = 2373
x463 = 1387 y463 = 2371
x464 = 1390 y464 = 2369
x465 = 1393 y465 = 2367
x466 = 1396 y466 = 2365
x467 = 1399 y467 = 2363
x468 = 1402 y468 = 2361
x469 = 1405 y469 = 2359
x470 = 1408 y470 = 2357
x471 = 1411 y471 = 2355
x472 = 1414 y472 = 2353
x473 = 1417 y473 = 2351
x474 = 1420 y474 = 2349
x475 = 1423 y475 = 2347
x476 = 1426 y476 = 2345
x477 = 1429 y477 = 2343
x478 = 1432 y478 = 2341
x479 = 1435 y479 = 2339
x480 = 1438 y480 = 2337
x481 = 1441 y481 = 2335
x482 = 1444 y482 = 2333
x483 = 1447 y483 = 2331
x484 = 1450 y484 = 2329
x485 = 1453 y485 = 2327
x486 = 1456 y486 = 2325
x487 = 1459 y487 = 2323
x488 = 1462 y488 = 2321
x489 = 1465 y489 = 2319
x490 = 1468 y490 = 2317
x491 = 1471 y491 = 2315
x492 = 1474 y492 = 2313
x493 = 1477 y493 = 2311
x494 = 1480 y494 = 2309
x495 = 1483 y495 = 2307
x496 = 1486 y496 = 2305
x497 = 1489 y497 = 2303
x498 = 1492 y498 = 2301
x499 = 1495 y499 = 2299
x500 = 1498 y500 = 2297
Rovnice píšte každú na nový riadok alebo oddelujte bodkočiarkou. Neznáme (premenné) označte jedným písmenom a-z napr. a,b alebo x,y,z apod. Diofantická rovnice (niekedy tiež diofantovská) v matematike je neurčitá polynomiálnej rovnica, ktorá dovoľuje premenlivým mať len hodnoty z odboru celých čísel. Diofantovské problémy majú menej rovníc než neznámych premenných a zahŕňajú nájdenie celých čísel, ktoré sú riešením pre všetky rovnice sústavy.
Príklady diofantových rovníc a problémov:
ab=12
5x+7y=144
8x=27y+38
54=ab 90=bc
(((x-1)*2/3-1)*2/3-1)*2/3=y