Thema: Je erste 3 Potenzzahlengleichungen p^a - q^b = r^c Main table of content: http://www.fermatquotient.com/ Nicht kürzbare (teilweise bis 6) Gleichungen Not simplify equations ; gcf(p,q,r) = 1 p^a - q^b = r^c ; p>1 ; q>1 ; r>1 ; ggT(p,q,r) = 1 Differenz-Zahlen, Differenz ; 2. Gleichung ; 3. Gleichung 13^2 - 12^2 = 5^2 ; 29^2 - 21^2 = 20^2 ; 37^2 - 35^2 = 12^2 ; 53^2 - 45^2 = 28^2 ; 61^2 - 60^2 = 11^2 ; 65^2 - 56^2 = 33^2 5^3 - 11^2 = 2^2 ; 14^2 - 13^2 = 3^3 ; 43^2 - 12^3 = 11^2 ; 55^2 - 53^2 = 6^3 ; 63^2 - 62^2 = 5^3 ; 17^3 - 52^2 = 47^2 5^2 - 2^4 = 3^2 ; 5^4 - 24^2 = 7^2 ; 41^2 - 40^2 = 3^4 ; 85^2 - 77^2 = 6^4 ; 145^2 - 12^4 = 17^2 ; 13^4 - 120^2 = 119^2 5^5 - 41^2 = 38^2 ; 251^2 - 235^2 = 6^5 ; 499^2 - 12^5 = 13^2 ; 13^5 - 597^2 = 122^2 ; 17^5 - 1121^2 = 404^2 ; 1563^2 - 1562^2 = 5^5 17^2 - 15^2 = 2^6 ; 5^6 - 117^2 = 44^2 ; 365^2 - 364^2 = 3^6 ; 745^2 - 713^2 = 6^6 ; 1753^2 - 12^6 = 295^2 ; 13^6 - 2035^2 = 828^2 33^2 - 31^2 = 2^7 ; 5^7 - 278^2 = 29^2 ; 1094^2 - 1093^2 = 3^7 65^2 - 63^2 = 2^8 ; 5^8 - 527^2 = 336^2 ; 3281^2 - 3280^2 = 3^8 129^2 - 127^2 = 2^9 ; 5^9 - 1199^2 = 718^2 ; 9842^2 - 9841^2 = 3^9 257^2 - 255^2 = 2^10 ; 5^10 - 3116^2 = 237^2 ; 29525^2 - 29524^2 = 3^10 513^2 - 511^2 = 2^11 ; 5^11 - 6469^2 = 2642^2 ; 88574^2 - 88573^2 = 3^11 1025^2 - 1023^2 = 2^12 ; 5^12 - 11753^2 = 10296^2 ; 265721^2 - 265720^2 = 3^12 2049^2 - 2047^2 = 2^13 ; 5^13 - 33802^2 = 8839^2 ; 797162^2 - 797161^2 = 3^13 4097^2 - 4095^2 = 2^14 ; 5^14 - 76443^2 = 16124^2 ; 2391485^2 - 2391484^2 = 3^14 8193^2 - 8191^2 = 2^15 ; 5^15 - 136762^2 = 108691^2 ; 7174454^2 - 7174453^2 = 3^15 16385^2 - 16383^2 = 2^16 ; 5^16 - 354144^2 = 164833^2 ; 21523361^2 - 21523360^2 = 3^16 32769^2 - 32767^2 = 2^17 ; 5^17 - 873121^2 = 24478^2 ; 64570082^2 - 64570081^2 = 3^17 65537^2 - 65535^2 = 2^18 ; 5^18 - 1721764^2 = 922077^2 ; 193710245^2 - 193710244^2 = 3^18 131073^2 - 131071^2 = 2^19 ; 5^19 - 3565918^2 = 2521451^2 ; 581130734^2 - 581130733^2 = 3^19 262145^2 - 262143^2 = 2^20 ; 5^20 - 9653287^2 = 1476984^2 ; 1743392201^2 - 1743392200^2 = 3^20 ... 228^2 - 37^3 = 11^3 ; 71^3 - 588^2 = 23^3 ; 74^3 - 549^2 = 47^3 ; 671^2 - 65^3 = 56^3 ; 105^3 - 104^3 = 181^2 ; 1261^2 - 112^3 = 57^3 29^2 - 5^4 = 6^3 ; 13^3 - 46^2 = 3^4 ; 76^2 - 15^3 = 7^4 ; 397^2 - 17^4 = 42^3 ; 42^4 - 143^3 = 433^2 ; 193^3 - 2681^2 = 6^4 7^3 - 3^5 = 10^2 ; 411^2 - 10^5 = 41^3 ; 19^5 - 127^3 = 654^2 ; 7792^2 - 393^3 = 7^5 ; 1153^3 - 39151^2 = 6^5 ; 1226^3 - 36599^2 = 55^5 71^2 - 17^3 = 2^7 ; 65^7 - 2213459^2 = 1414^3 ; 113^7 - 15312283^2 = 9262^3 ; 21063928^2 - 76271^3 = 17^7 15613^3 - 1549034^2 = 33^8 ; 30042907^2 - 96222^3 = 43^8 2^9 - 7^3 = 13^2 3^4 - 7^2 = 2^5 ; 122^2 - 11^4 = 3^5 Kürzbare Gleichungen mit 1 Quadrat bis 2E+25 durchsucht Simplify equations by 1 square ; gcf(p,q,r) > 1 p^a - q^b = r^c ; p>2 ; q>2 ; r>2 ; ggT(p,q,r) > 1 Differenz-Zahlen, Differenz ; 2. Gleichung ; 3. Gleichung 375^2 - 50^3 = 5^6 ; 648^2 - 72^3 = 6^6 ; 1029^2 - 98^3 = 7^6 12^3 - 40^2 = 2^7 ; 12^7 - 288^3 = 3456^2 ; 363^3 - 5324^2 = 11^7 20^3 - 88^2 = 2^8 ; 405^2 - 54^3 = 3^8 ; 6831^2 - 360^3 = 3^8 2496^2 - 184^3 = 2^9 ; 360^3 - 6048^2 = 6^9 ; 392^3 - 7^9 = 4459^2 117^3 - 1242^2 = 3^10 ; 3625^2 - 5^10 = 150^3 ; 6^10 - 6048^2 = 288^3 63^3 - 3^11 = 270^2 ; 6^11 - 18872^2 = 188^3 ; 411000^2 - 10^11 = 4100^3 46875^2 - 1250^3 = 5^12 ; 139968^2 - 2592^3 = 6^12 ; 352947^2 - 4802^3 = 7^12 48^3 - 320^2 = 2^13 ; 568^2 - 68^3 = 2^13 ; 12^13 - 41472^3 = 5971968^2 80^3 - 704^2 = 2^14 ; 10935^2 - 486^3 = 3^14 ; 184437^2 - 3240^3 = 3^14 2^15 - 28^3 = 104^2 ; 19968^2 - 736^3 = 2^15 ; 12960^3 - 1306368^2 = 6^15 1053^3 - 33534^2 = 3^16 ; 453125^2 - 5^16 = 3750^3 ; 6^16 - 1306368^2 = 10368^3 567^3 - 3^17 = 7290^2 ; 6^17 - 4076352^2 = 6768^3 ; 411000000^2 - 10^17 = 410000^3 5859375^2 - 31250^3 = 5^18 ; 30233088^2 - 93312^3 = 6^18 ; 121060821^2 - 235298^3 = 7^18 192^3 - 2560^2 = 2^19 ; 4544^2 - 272^3 = 2^19 ; 3764768^3 - 7304002867^2 = 7^19 320^3 - 5632^2 = 2^20 ; 295245^2 - 4374^3 = 3^20 ; 4979799^2 - 29160^3 = 3^20 2^21 - 112^3 = 832^2 ; 159744^2 - 2944^3 = 2^21 ; 466560^3 - 282175488^2 = 6^21 9477^3 - 905418^2 = 3^22 ; 56640625^2 - 5^22 = 93750^3 ; 1269531250^2 - 1171875^3 = 5^22 5103^3 - 3^23 = 196830^2 ; 6^23 - 880492032^2 = 243648^3 ; 314435305744^2 - 46236057^3 = 7^23 732421875^2 - 781250^3 = 5^24 ; 6530347008^2 - 3359232^3 = 6^24 ; 41523861603^2 - 11529602^3 = 7^24 768^3 - 20480^2 = 2^25 ; 36352^2 - 1088^3 = 2^25 ; 184473632^3 - 2505272983381^2 = 7^25 1280^3 - 45056^2 = 2^26 ; 7971615^2 - 39366^3 = 3^26 ; 134454573^2 - 262440^3 = 3^26 2^27 - 448^3 = 6656^2 ; 1277952^2 - 11776^3 = 2^27 ; 16796160^3 - 60949905408^2 = 6^27 85293^3 - 24446286^2 = 3^28 ; 7080078125^2 - 5^28 = 2343750^3 ; 6^28 - 60949905408^2 = 13436928^3 45927^3 - 3^29 = 5314410^2 ; 6^29 - 190186278912^2 = 8771328^3 91552734375^2 - 19531250^3 = 5^30 ; 1410554953728^2 - 120932352^3 = 6^30 3072^3 - 163840^2 = 2^31 ; 290816^2 - 4352^3 = 2^31 5120^3 - 360448^2 = 2^32 ; 215233605^2 - 354294^3 = 3^32 ; 3630273471^2 - 2361960^3 = 3^32 2^33 - 1792^3 = 53248^2 ; 10223616^2 - 47104^3 = 2^33 767637^3 - 660049722^2 = 3^34 ; 885009765625^2 - 5^34 = 58593750^3 413343^3 - 3^35 = 143489070^2 12288^3 - 1310720^2 = 2^37 ; 2326528^2 - 17408^3 = 2^37 20480^3 - 2883584^2 = 2^38 ; 5811307335^2 - 3188646^3 = 3^38 ; 98017383717^2 - 21257640^3 = 3^38 2^39 - 7168^3 = 425984^2 ; 81788928^2 - 188416^3 = 2^39 6908733^3 - 17821342494^2 = 3^40 3720087^3 - 3^41 = 3874204890^2 49152^3 - 10485760^2 = 2^43 ; 18612224^2 - 69632^3 = 2^43 81920^3 - 23068672^2 = 2^44 ; 156905298045^2 - 28697814^3 = 3^44 ; 2646469360359^2 - 191318760^3 = 3^44 2^45 - 28672^3 = 3407872^2 ; 654311424^2 - 753664^3 = 2^45 62178597^3 - 481176247338^2 = 3^46 33480783^3 - 3^47 = 104603532030^2 196608^3 - 83886080^2 = 2^49 ; 148897792^2 - 278528^3 = 2^49 327680^3 - 184549376^2 = 2^50 ; 4236443047215^2 - 258280326^3 = 3^50 2^51 - 114688^3 = 27262976^2 ; 5234491392^2 - 3014656^3 = 2^51 786432^3 - 671088640^2 = 2^55 ; 1191182336^2 - 1114112^3 = 2^55 1310720^3 - 1476395008^2 = 2^56 2^57 - 458752^3 = 218103808^2 ; 41875931136^2 - 12058624^3 = 2^57 3145728^3 - 5368709120^2 = 2^61 ; 9529458688^2 - 4456448^3 = 2^61 5242880^3 - 11811160064^2 = 2^62 2^63 - 1835008^3 = 1744830464^2 ; 335007449088^2 - 48234496^3 = 2^63 12582912^3 - 42949672960^2 = 2^67 ; 76235669504^2 - 17825792^3 = 2^67 20971520^3 - 94489280512^2 = 2^68 2^69 - 7340032^3 = 13958643712^2 ; 2680059592704^2 - 192937984^3 = 2^69 50331648^3 - 343597383680^2 = 2^73 ; 609885356032^2 - 71303168^3 = 2^73 83886080^3 - 755914244096^2 = 2^74 2^75 - 29360128^3 = 111669149696^2 201326592^3 - 2748779069440^2 = 2^79 2^81 - 117440512^3 = 893353197568^2 18^2 - 3^5 = 3^4 ; 5^5 - 50^2 = 5^4 ; 14^4 - 147^2 = 7^5 45^2 - 6^4 = 3^6 ; 5^6 - 10^4 = 75^2 ; 15^4 - 6^6 = 63^2 12^2 - 2^7 = 2^4 ; 1044^2 - 30^4 = 6^7 ; 13^7 - 7774^2 = 39^4 6^4 - 28^2 = 2^9 ; 1098^2 - 33^4 = 3^9 ; 90^4 - 7452^2 = 6^9 405^2 - 18^4 = 3^10 ; 5^10 - 50^4 = 1875^2 ; 90^4 - 6^10 = 2268^2 37584^2 - 180^4 = 6^11 ; 13^11 - 1313806^2 = 507^4 ; 2052855^2 - 14^11 = 637^4 12^4 - 112^2 = 2^13 ; 9882^2 - 99^4 = 3^13 ; 540^4 - 268272^2 = 6^13 3645^2 - 54^4 = 3^14 ; 5^14 - 250^4 = 46875^2 ; 540^4 - 6^14 = 81648^2 1353024^2 - 1080^4 = 6^15 ; 13^15 - 222033214^2 = 6591^4 ; 402359580^2 - 14^15 = 8918^4 24^4 - 448^2 = 2^17 ; 88938^2 - 297^4 = 3^17 ; 3240^4 - 9657792^2 = 6^17 32805^2 - 162^4 = 3^18 ; 5^18 - 1250^4 = 1171875^2 ; 3240^4 - 6^18 = 2939328^2 48708864^2 - 6480^4 = 6^19 ; 13^19 - 37523613166^2 = 85683^4 ; 78862477680^2 - 14^19 = 124852^4 48^4 - 1792^2 = 2^21 ; 800442^2 - 891^4 = 3^21 ; 19440^4 - 347680512^2 = 6^21 295245^2 - 486^4 = 3^22 ; 5^22 - 6250^4 = 29296875^2 ; 19440^4 - 6^22 = 105815808^2 1753519104^2 - 38880^4 = 6^23 96^4 - 7168^2 = 2^25 ; 7203978^2 - 2673^4 = 3^25 ; 116640^4 - 12516498432^2 = 6^25 2657205^2 - 1458^4 = 3^26 ; 5^26 - 31250^4 = 732421875^2 ; 116640^4 - 6^26 = 3809369088^2 63126687744^2 - 233280^4 = 6^27 192^4 - 28672^2 = 2^29 ; 64835802^2 - 8019^4 = 3^29 ; 699840^4 - 450593943552^2 = 6^29 23914845^2 - 4374^4 = 3^30 ; 5^30 - 156250^4 = 18310546875^2 ; 699840^4 - 6^30 = 137137287168^2 2272560758784^2 - 1399680^4 = 6^31 384^4 - 114688^2 = 2^33 ; 583522218^2 - 24057^4 = 3^33 215233605^2 - 13122^4 = 3^34 ; 5^34 - 781250^4 = 457763671875^2 768^4 - 458752^2 = 2^37 ; 5251699962^2 - 72171^4 = 3^37 1937102445^2 - 39366^4 = 3^38 1536^4 - 1835008^2 = 2^41 ; 47265299658^2 - 216513^4 = 3^41 17433922005^2 - 118098^4 = 3^42 3072^4 - 7340032^2 = 2^45 ; 425387696922^2 - 649539^4 = 3^45 156905298045^2 - 354294^4 = 3^46 6144^4 - 29360128^2 = 2^49 ; 3828489272298^2 - 1948617^4 = 3^49 1412147682405^2 - 1062882^4 = 3^50 12288^4 - 117440512^2 = 2^53 24576^4 - 469762048^2 = 2^57 49152^4 - 1879048192^2 = 2^61 98304^4 - 7516192768^2 = 2^65 196608^4 - 30064771072^2 = 2^69 393216^4 - 120259084288^2 = 2^73 786432^4 - 481036337152^2 = 2^77 1572864^4 - 1924145348608^2 = 2^81 6^5 - 88^2 = 2^5 ; 6655^2 - 33^5 = 22^5 ; 54^5 - 21384^2 = 18^5 29760696^2 - 972^5 = 162^6 ; 660^6 - 252504000^2 = 1800^5 ; 556950168^2 - 810^6 = 1944^5 297^5 - 1519965^2 = 18^7 ; 432^5 - 72^7 = 2239488^2 ; 108^7 - 648^5 = 7558272^2 1377^2 - 18^5 = 3^8 ; 42^8 - 392^5 = 653072^2 ; 800^5 - 17920000^2 = 40^8 98^5 - 84035^2 = 7^11 ; 392^5 - 3042067^2 = 7^11 ; 5940688^2 - 507^5 = 13^11 6^12 - 72^5 = 15552^2 ; 151263^2 - 7^12 = 98^5 ; 500^5 - 5500000^2 = 10^12 7^13 - 147^5 = 168070^2 ; 6272^5 - 28^13 = 1789878272^2 ; 47616898611^2 - 16810^5 = 41^13 3^14 - 1701^2 = 18^5 ; 12353145^2 - 686^5 = 7^14 ; 19648222^2 - 11^14 = 363^5 24^5 - 2816^2 = 2^15 ; 6^15 - 684288^2 = 72^5 ; 24^15 - 22422749184^2 = 4608^5 96228^5 - 2872077225120^2 = 18^17 334611^2 - 162^5 = 3^18 4802^5 - 1412376245^2 = 7^21 ; 19208^5 - 51128020069^2 = 7^21 ; 1452495777656^2 - 73205^5 = 11^21 6^22 - 2592^5 = 120932352^2 ; 50000^5 - 550000000000^2 = 10^22 7^23 - 7203^5 = 2824752490^2 3^24 - 413343^2 = 162^5 ; 207619308015^2 - 33614^5 = 7^24 ; 3164365801322^2 - 11^24 = 43923^5 96^5 - 90112^2 = 2^25 ; 6^25 - 5321023488^2 = 2592^5 81310473^2 - 1458^5 = 3^28 6^32 - 93312^5 = 940369969152^2 3^34 - 100442349^2 = 1458^5 384^5 - 2883584^2 = 2^35 19758444939^2 - 13122^5 = 3^38 3^44 - 24407490807^2 = 13122^5 1536^5 - 92274688^2 = 2^45 6144^5 - 2952790016^2 = 2^55 24576^5 - 94489280512^2 = 2^65 98304^5 - 3023656976384^2 = 2^75 54^2 - 3^7 = 3^6 ; 5^7 - 250^2 = 5^6 ; 10^7 - 3000^2 = 10^6 2160^2 - 12^6 = 6^8 ; 10^8 - 20^6 = 6000^2 ; 57375^2 - 15^8 = 30^6 24^2 - 2^9 = 2^6 ; 472392^2 - 18^9 = 54^6 ; 46875000^2 - 50^9 = 250^6 9720^2 - 6^10 = 18^6 ; 50^6 - 10^10 = 75000^2 ; 15^10 - 90^6 = 212625^2 2592^6 - 72^11 = 5804752896^2 ; 142367525496^2 - 4802^6 = 98^11 ; 1422608035608^2 - 162^11 = 4374^6 4625000^2 - 150^6 = 10^13 ; 450^6 - 79734375^2 = 15^13 ; 3129311232^2 - 1440^6 = 24^13 466560^2 - 72^6 = 6^14 ; 10^14 - 200^6 = 6000000^2 ; 193640625^2 - 15^14 = 450^6 2099520^2 - 6^16 = 108^6 ; 500^6 - 10^16 = 75000000^2 ; 15^16 - 1350^6 = 717609375^2 4625000000^2 - 1500^6 = 10^19 ; 6750^6 - 269103515625^2 = 15^19 ; 1067290888473^2 - 9826^6 = 17^19 100776960^2 - 432^6 = 6^20 ; 10^20 - 2000^6 = 6000000000^2 ; 653537109375^2 - 15^20 = 6750^6 453496320^2 - 6^22 = 648^6 ; 5000^6 - 10^22 = 75000000000^2 4625000000000^2 - 15000^6 = 10^25 21767823360^2 - 2592^6 = 6^26 97955205120^2 - 6^28 = 3888^6 4701849845760^2 - 15552^6 = 6^32 1016^7 - 33298514048^2 = 508^7 ; 35446128768^2 - 1032^7 = 516^7 ; 144429158167^2 - 1516^7 = 1137^7 13226976^2 - 108^7 = 18^10 ; 2812500000^2 - 500^7 = 50^10 ; 1352^7 - 90868763648^2 = 52^10 3200^7 - 1835008000000^2 = 80^12 98^7 - 9058973^2 = 7^15 ; 117234820736^2 - 1452^7 = 22^15 ; 1568^7 - 134929285120^2 = 28^15 12^16 - 288^7 = 143327232^2 ; 1897443072^2 - 14^16 = 392^7 ; 18^16 - 8571080448^2 = 648^7 12^17 - 1433272320^2 = 288^7 ; 29134045783^2 - 17^17 = 578^7 790224609375^2 - 15^20 = 2250^7 162^2 - 3^9 = 3^8 ; 5^9 - 1250^2 = 5^8 ; 10^9 - 30000^2 = 10^8 414720^2 - 24^8 = 12^10 ; 20^10 - 40^8 = 1920000^2 ; 27540000^2 - 30^10 = 60^8 48^2 - 2^11 = 2^8 ; 54^8 - 18^11 = 2834352^2 ; 20^11 - 14080000^2 = 40^8 144551952^2 - 18^13 = 54^8 44789760^2 - 12^14 = 72^8 ; 200^8 - 20^14 = 960000000^2 ; 46473750000^2 - 450^8 = 30^14 8599633920^2 - 288^8 = 12^18 ; 20^18 - 800^8 = 307200000000^2 972^8 - 18^19 = 297538935552^2 ; 20^19 - 2252800000000^2 = 800^8 928760463360^2 - 12^22 = 864^8 1805076171^2 - 114^9 = 57^9 ; 924198999552^2 - 456^9 = 228^9 2727521159431^2 - 578^9 = 17^19 98^9 - 7^21 = 524596891^2 6^22 - 282175488^2 = 72^9 486^2 - 3^11 = 3^10 ; 5^11 - 6250^2 = 5^10 ; 10^11 - 300000^2 = 10^10 318504960^2 - 48^10 = 24^12 ; 40^12 - 80^10 = 2457600000^2 ; 52876800000^2 - 60^12 = 120^10 96^2 - 2^13 = 2^10 765275040^2 - 18^14 = 54^10 ; 250^10 - 50^14 = 585937500000^2 18366600960^2 - 108^10 = 18^16 ; 3302259425280^2 - 24^18 = 288^10 1458^2 - 3^13 = 3^12 ; 5^13 - 31250^2 = 5^12 ; 10^13 - 3000000^2 = 10^12 978447237120^2 - 96^12 = 48^14 192^2 - 2^15 = 2^12 4374^2 - 3^15 = 3^14 ; 5^15 - 156250^2 = 5^14 ; 10^15 - 30000000^2 = 10^14 384^2 - 2^17 = 2^14 54^14 - 1041386274432^2 = 18^19 13122^2 - 3^17 = 3^16 ; 5^17 - 781250^2 = 5^16 ; 10^17 - 300000000^2 = 10^16 768^2 - 2^19 = 2^16 39366^2 - 3^19 = 3^18 ; 5^19 - 3906250^2 = 5^18 ; 10^19 - 3000000000^2 = 10^18 1536^2 - 2^21 = 2^18 118098^2 - 3^21 = 3^20 ; 5^21 - 19531250^2 = 5^20 ; 10^21 - 30000000000^2 = 10^20 3072^2 - 2^23 = 2^20 354294^2 - 3^23 = 3^22 ; 5^23 - 97656250^2 = 5^22 ; 10^23 - 300000000000^2 = 10^22 6144^2 - 2^25 = 2^22 1062882^2 - 3^25 = 3^24 ; 5^25 - 488281250^2 = 5^24 ; 10^25 - 3000000000000^2 = 10^24 12288^2 - 2^27 = 2^24 3188646^2 - 3^27 = 3^26 ; 5^27 - 2441406250^2 = 5^26 24576^2 - 2^29 = 2^26 9565938^2 - 3^29 = 3^28 ; 5^29 - 12207031250^2 = 5^28 49152^2 - 2^31 = 2^28 28697814^2 - 3^31 = 3^30 ; 5^31 - 61035156250^2 = 5^30 98304^2 - 2^33 = 2^30 86093442^2 - 3^33 = 3^32 ; 5^33 - 305175781250^2 = 5^32 196608^2 - 2^35 = 2^32 258280326^2 - 3^35 = 3^34 ; 5^35 - 1525878906250^2 = 5^34 393216^2 - 2^37 = 2^34 774840978^2 - 3^37 = 3^36 786432^2 - 2^39 = 2^36 2324522934^2 - 3^39 = 3^38 1572864^2 - 2^41 = 2^38 6973568802^2 - 3^41 = 3^40 3145728^2 - 2^43 = 2^40 20920706406^2 - 3^43 = 3^42 6291456^2 - 2^45 = 2^42 62762119218^2 - 3^45 = 3^44 12582912^2 - 2^47 = 2^44 188286357654^2 - 3^47 = 3^46 25165824^2 - 2^49 = 2^46 564859072962^2 - 3^49 = 3^48 50331648^2 - 2^51 = 2^48 1694577218886^2 - 3^51 = 3^50 100663296^2 - 2^53 = 2^50 5083731656658^2 - 3^53 = 3^52 201326592^2 - 2^55 = 2^52 402653184^2 - 2^57 = 2^54 805306368^2 - 2^59 = 2^56 1610612736^2 - 2^61 = 2^58 3221225472^2 - 2^63 = 2^60 6442450944^2 - 2^65 = 2^62 12884901888^2 - 2^67 = 2^64 25769803776^2 - 2^69 = 2^66 51539607552^2 - 2^71 = 2^68 103079215104^2 - 2^73 = 2^70 206158430208^2 - 2^75 = 2^72 412316860416^2 - 2^77 = 2^74 824633720832^2 - 2^79 = 2^76 1649267441664^2 - 2^81 = 2^78 3298534883328^2 - 2^83 = 2^80 Kürzbare Gleichungen bis 2E+25 durchsucht Simplify equations ; gcf(p,q,r) > 1 ; without 2^(n+1) - 2^n = 2^n p^a - q^b = r^c ; a>2 ; b>2 ; c>2 ; ggT(p,q,r) > 1 ; ohne 2^(n+1) - 2^n = 2^n Differenz-Zahlen, Differenz ; 2. Gleichung ; 3. Gleichung 14^3 - 7^4 = 7^3 ; 57^3 - 19^4 = 38^3 ; 78^3 - 26^4 = 26^3 3^5 - 6^3 = 3^3 ; 104^3 - 91^3 = 13^5 ; 24^5 - 192^3 = 96^3 1083^3 - 19^7 = 722^3 ; 35^7 - 3675^3 = 2450^3 ; 54^7 - 8748^3 = 8748^3 1352^3 - 1183^3 = 13^8 ; 7840^3 - 28^8 = 4704^3 ; 15225^3 - 35^8 = 10850^3 20577^3 - 19^10 = 13718^3 ; 35^10 - 128625^3 = 85750^3 ; 202612^3 - 37^10 = 151959^3 219520^3 - 28^11 = 131712^3 ; 532875^3 - 35^11 = 379750^3 ; 98^11 - 19765032^3 = 6588344^3 390963^3 - 19^13 = 260642^3 ; 35^13 - 4501875^3 = 3001250^3 ; 54^13 - 25509168^3 = 25509168^3 228488^3 - 199927^3 = 13^14 ; 6146560^3 - 28^14 = 3687936^3 ; 18650625^3 - 35^14 = 13291250^3 7428297^3 - 19^16 = 4952198^3 ; 35^16 - 157565625^3 = 105043750^3 2970344^3 - 2599051^3 = 13^17 ; 24^17 - 63700992^3 = 31850496^3 ; 172103680^3 - 28^17 = 103262208^3 141137643^3 - 19^19 = 94091762^3 648^3 - 108^4 = 108^4 ; 5000^3 - 500^4 = 500^4 ; 630^4 - 5400^3 = 90^4 2592^4 - 31104^3 = 432^5 ; 69984^3 - 3888^4 = 648^5 ; 559872^3 - 2592^5 = 15552^4 72^4 - 288^3 = 12^6 ; 1125^4 - 11250^3 = 75^6 ; 1944^4 - 23328^3 = 108^6 7558272^3 - 139968^4 = 648^7 300^4 - 2000^3 = 10^8 ; 60^8 - 54000^3 = 1800^4 ; 78608^3 - 68^8 = 2312^4 62208^4 - 2239488^3 = 72^10 ; 80000000^3 - 800000^4 = 200^10 ; 288^10 - 143327232^3 = 995328^4 43923^3 - 2662^4 = 11^13 ; 24^13 - 27648^4 = 663552^3 ; 43^13 - 10256403^3 = 159014^4 29^14 - 121945^4 = 4243686^3 ; 131712^4 - 28^14 = 4917248^3 ; 58206928^3 - 46^14 = 292008^4 14^15 - 19208^4 = 268912^3 124416^4 - 5971968^3 = 12^18 300000^4 - 20000000^3 = 10^20 972^3 - 54^5 = 54^5 ; 12500^3 - 250^5 = 250^5 ; 496^5 - 30752^3 = 248^5 72^8 - 864^5 = 62208^3 ; 3981312^3 - 288^8 = 6912^5 ; 41006250^3 - 675^8 = 30375^5 28^9 - 392^5 = 10976^3 ; 658464^3 - 2888^5 = 76^9 ; 9800^5 - 4116000^3 = 140^9 5808^5 - 1874048^3 = 44^10 250^5 - 9375^3 = 5^16 ; 27648^5 - 24^16 = 15925248^3 ; 55296^5 - 79626240^3 = 24^16 700000^3 - 3000^5 = 10^17 648^5 - 6^18 = 23328^3 31250^5 - 29296875^3 = 5^31 98^3 - 7^7 = 7^6 ; 74^6 - 37^7 = 4107^3 ; 2028^3 - 26^7 = 26^6 3^8 - 18^3 = 3^6 ; 24^8 - 4608^3 = 48^6 ; 192^8 - 1179648^3 = 768^6 72^10 - 1492992^3 = 864^6 2738^6 - 37^13 = 5622483^3 ; 6272^6 - 56^13 = 19668992^3 ; 69229205^3 - 7442^6 = 61^13 24^14 - 2654208^3 = 1152^6 69984^3 - 108^7 = 108^7 ; 2500000^3 - 500^7 = 500^7 ; 8957952^3 - 864^7 = 864^7 864^7 - 72^11 = 4478976^3 72^7 - 12^12 = 10368^3 54^7 - 10935^3 = 3^22 ; 130000000^3 - 3000^7 = 10^22 1458^7 - 23914845^3 = 3^43 52488^3 - 54^8 = 54^8 ; 3125000^3 - 250^8 = 250^8 ; 13436928^3 - 432^8 = 432^8 686^3 - 7^10 = 7^9 ; 52728^3 - 26^10 = 26^9 ; 28^10 - 65856^3 = 28^9 3^11 - 54^3 = 3^9 ; 26^9 - 15379^3 = 13^11 ; 24^11 - 48^9 = 55296^3 338^9 - 33787663^3 = 13^20 7558272^3 - 108^10 = 108^10 2834352^3 - 54^11 = 54^11 4802^3 - 7^13 = 7^12 ; 1370928^3 - 26^13 = 26^12 ; 28^13 - 1843968^3 = 28^12 3^14 - 162^3 = 3^12 153055008^3 - 54^14 = 54^14 33614^3 - 7^16 = 7^15 ; 35644128^3 - 26^16 = 26^15 ; 28^16 - 51631104^3 = 28^15 3^17 - 486^3 = 3^15 235298^3 - 7^19 = 7^18 3^20 - 1458^3 = 3^18 1647086^3 - 7^22 = 7^21 3^23 - 4374^3 = 3^21 11529602^3 - 7^25 = 7^24 3^26 - 13122^3 = 3^24 80707214^3 - 7^28 = 7^27 3^29 - 39366^3 = 3^27 3^32 - 118098^3 = 3^30 3^35 - 354294^3 = 3^33 3^38 - 1062882^3 = 3^36 3^41 - 3188646^3 = 3^39 3^44 - 9565938^3 = 3^42 3^47 - 28697814^3 = 3^45 3^50 - 86093442^3 = 3^48 3^53 - 258280326^3 = 3^51 30^4 - 15^5 = 15^4 ; 17^5 - 34^4 = 17^4 ; 85^4 - 34^5 = 51^4 648^7 - 69984^4 = 69984^4 ; 600000^4 - 2000^7 = 200000^4 ; 600000^4 - 2000^7 = 200000^4 2890^4 - 34^9 = 1734^4 ; 12675^4 - 65^9 = 8450^4 ; 97^9 - 28227^4 = 18818^4 98260^4 - 34^13 = 58956^4 ; 823875^4 - 65^13 = 549250^4 3888^4 - 648^5 = 648^5 ; 2904^5 - 21296^4 = 968^5 ; 50000^4 - 5000^5 = 5000^5 8748^6 - 52488^5 = 472392^4 864^7 - 124416^4 = 10368^5 ; 629856^4 - 1944^7 = 34992^5 127575^4 - 12150^5 = 135^8 ; 750000^4 - 50000^5 = 500^8 1485172^4 - 85683^5 = 13^21 50421^4 - 7^22 = 4802^5 15552^4 - 72^9 = 432^6 14739^4 - 578^6 = 17^13 ; 4608^6 - 48^13 = 221184^4 ; 80^13 - 12800^6 = 1024000^4 45^14 - 546750^4 = 6075^6 52488^4 - 18^15 = 972^6 8748^4 - 162^7 = 162^7 ; 312500^4 - 1250^7 = 1250^7 ; 1119744^4 - 2592^7 = 2592^7 72^10 - 432^7 = 31104^4 ; 2000^7 - 200^10 = 400000^4 450^4 - 15^9 = 15^8 ; 17^9 - 578^4 = 17^8 ; 350^8 - 175^9 = 91875^4 1417176^4 - 162^11 = 162^11 6750^4 - 15^13 = 15^12 ; 17^13 - 9826^4 = 17^12 ; 1536000^4 - 80^13 = 80^12 101250^4 - 15^17 = 15^16 ; 17^17 - 167042^4 = 17^16 1518750^4 - 15^21 = 15^20 62^5 - 31^6 = 31^5 ; 33^6 - 66^5 = 33^5 ; 633^5 - 211^6 = 422^5 528^5 - 88^7 = 176^5 ; 1944^7 - 34992^5 = 34992^5 ; 67584^5 - 2816^7 = 22528^5 972^8 - 52488^5 = 52488^5 46464^5 - 88^12 = 15488^5 432^8 - 15552^5 = 2592^6 ; 10368^6 - 62208^5 = 864^8 41472^5 - 6912^6 = 288^9 17496^5 - 972^7 = 972^7 78732^5 - 486^9 = 486^9 1922^5 - 31^11 = 31^10 ; 33^11 - 2178^5 = 33^10 59582^5 - 31^16 = 31^15 ; 33^16 - 71874^5 = 33^15 126^6 - 63^7 = 63^6 ; 65^7 - 130^6 = 65^6 ; 1995^6 - 665^7 = 1330^6 7938^6 - 63^13 = 63^12 ; 65^13 - 8450^6 = 65^12 254^7 - 127^8 = 127^7 ; 129^8 - 258^7 = 129^7 510^8 - 255^9 = 255^8 ; 257^9 - 514^8 = 257^8 Ende der Suche für eine längere Zeit 29.06.2009 Richard Fischer