x^4 + y^3 = k*z^2, k is a small prime

 
 
x^4 \; + \; y^3 \; = \; z^2

2^4 \; + \; 0^3 \; = \; 4^2
7^4 \; + \; 15^3 \; = \; 76^2
26^4 \; + \; 224^3 \; = \; 3420^2
97^4 \; + \; 3135^3 \; = \; 175784^2
362^4 \; + \; 43680^3 \; = \; 9129956^2
1351^4 \; + \; 608399^3 \; = \; 474554340^2
5042^4 \; + \; 8473920^3 \; = \; 24667592764^2
18817^4 \; + \; 118026495^3 \; = \; 1282239885136^2
70226^4 \; + \; 1643897024^3 \; = \; 66651805000260^2
262087^4 \; + \; 22896531855^3 \; = \; 3464611614776444^2
……………………………………………..
……………………………………………..
 
 
x^4 \; + \; y^3 \; = \; 2 \, z^2

5^4 \; + \; 7^3 \; = \; 2 \; \times \; 22^2
49^4 \; + \; 799^3 \; = \; 2 \; \times \; 16060^2
485^4 \; + \; 78407^3 \; = \; 2 \; \times \; 15525378^2
4801^4 \; + \; 7683199^3 \; = \; 2 \; \times \; 15059077880^2
47525^4 \; + \; 752875207^3 \; = \; 2 \; \times \; 14607284843822^2
470449^4 \; + \; 73774087199^3 \; = \; 2 \; \times \; 14169051188208180^2
………………………………………………………

 
 
x^4 \; + \; y^3 \; = \; 3 \, z^2
 
 

x^4 \; + \; y^3 \; = \; 5 \, z^2

4^4 \; + \; 4^3 = 5\; \times \; 8^2
31^4 \; + \; 319^3 = 5\; \times \; 2584^2
244^4 \; + \; 19844^3 = 5\; \times \; 1250424^2
1921^4 \; + \; 1230079^3 = 5\; \times \; 610121168^2
15124^4 \; + \; 76245124^3 = 5\; \times \; 297737224840^2
119071^4 \; + \; 4725967679^3 = 5\; \times \; 145295150446152^2
………………………………………..
 

x^4 \; + \; y^3 \; = \; 7 \, z^2

55^4 \; + \; 1007^3 \; = \; 7\; \times \; 12132^2
6049^4 \; + \; 12196799^3 \; = \; 7\; \times \; 16099779960^2
665335^4 \; + \; 147556887407^3 \; = \; 7\; \times \; 21423489369428268^2
……………………………………
 

x^4 \; + \; y^3 \; = \; 11 \, z^2

23^4 \; + \; 175^3 \; = \; 11\; \times \; 716^2
1057^4 \; + \; 372415^3 \; = \; 11\; \times \; 68525096^2
48599^4 \; + \; 787287599^3 \; = \; 11\; \times \; 6660453121380^2
………………………………………….
 

x^4 \; + \; y^3 \; = \; 13 \, z^2

25^4 \; + \; 207^3 \; = \; 13\; \times \; 844^2
1249^4 \; + \; 519999^3 \; = \; 13\; \times \; 104000600^2
62425^4 \; + \; 1298960207^3 \; = \; 13\; \times \; 12984406269156^2
…………………………………………….
 

x^4 \; + \; y^3 \; = \; 17 \, z^2

50^4 \; + \; 832^3 \; = \; 17\; \times \; 5852^2
4999^4 \; + \; 8329999^3 \; = \; 17\; \times \; 5831002100^2
499850^4 \; + \; 83283340832^3 \; = \; 17\; \times \; 5829250875134148^2
………………………………………………..
 

x^4 \; + \; y^3 \; = \; 19 \, z^2

151^4 \; + \; 7599^3 \; = \; 19\; \times \; 152060^2
45601^4 \; + \; 693150399^3 \; = \; 19\; \times \; 4186628434120^2
13771351^4 \; + \; 63216702788399^3 \; = \; 19\; \times \; 115311058888214376180^2
……………………………………………
 

x^4 \; + \; y^3 \; = \; 23 \, z^2

7775^4 \; + \; 20150207^3 \; = \; 23\times 18860597496^2
120901249^4 \; + \; 4872370669919999^3 \; = \; 23\times 70916380626551659664400^2
1880014414175^4 + 1178151399168589480310207^3 = 23\times 266647635558075525290896614856182504^2
………………………………………………………………..
 

x^4 \; + \; y^3 \; = \; 29 \, z^2

28^4 \; + \; 260^3 \; = \; 29\; \times \; 792^2
1567^4 \; + \; 818495^3 \; = \; 29\; \times \; 137507832^2
87724^4 \; + \; 2565166724^3 \; = \; 29\; \times \; 24125393076840^2
………………………………………………………………………….
 

x^4 \; + \; y^3 \; = \; 31 \, z^2

12151^4 + 49215599^3 = 31\times 62011659780^2
295293601^4 + 29066103597182399^3 = 31\times 890019206519595714709560^2
7176225079351^4 + 17166068796502088748860399^3 = 31\times 12773956301859998420087515904980739340^2
…………………………………………..
 

x^4 \; + \; y^3 \; = \; 37 \, z^2

295^4 + 29007^3 \; = \; 37\times 812308^2
174049^4 + 10097684799^3 \; = \; 37\times 166813752945560^2
102688615^4 + 3514983883539407^3 \; = \; 37\times 34259746496533192031292^2
……………………………………………………………..
 

x^4 \; + \; y^3 \; = \; 41 \, z^2

122^4 + 4960^3 \; = \; 41\times 54604^2
29767^4 + 295358095^3 \; = \; 41\times 792741137716^2
7263026^4 + 17583848892224^3 \; = \; 41\times 11515398881786733780^2
……………………………………………………….
 

x^4 \; + \; y^3 \; = \; 43 \, z^2

16855^4 + 94697007^3 = 43\times 140530364324^2
568182049^4 + 107610280268612799^3 = 43\times 5383273141016727382268920^2
19153416854935^4 + 122284459072969382277951407^3 = 43\times 206216149027737325382756300926561834476^2
……………………………………………….
 

x^4 \; + \; y^3 \; = \; 47 \, z^2

95^4 + 3007^3 = 47\times 24088^2
18049^4 + 108588799^3 = 47\times 165054980560^2
3429215^4 + 3919838505407^3 = 47\times 1132018001654653512^2
………………………………………………..
 

x^4 \; + \; y^3 \; = \; 53 \, z^2

1324^4 + 584324^3 = 53\times 61354440^2
3505951^4 + 4097230804799^3 = 53\times 1139194052967426120^2
9283756924^4 + 28729380874639313924^3 = 53\times 21152001354017733071216923320^2
………………………………………………..
 

x^4 \; + \; y^3 \; = \; 59 \, z^2

62423^4 + 1298876975^3 = 59\times 6094330785468^2

7793261857^4 + 20244976790590362815^3 = 59\times 11859050515291624496062100808^2

972957569736599^4 + 315548810835916302092746695599^3
= 59\times 23076705937483402089390802748364982542380340^2
………………………………………………..
 

x^4 \; + \; y^3 \; = \; 61 \, z^2

487^4 + 79055^3 = 61\times 2846124^2

474337^4 + 74998529855^3 = 61\times 2629748450975976^2

462003751^4 + 71149155312689999^3
= 61\times 2429907296985582789456900^2
……………………………………………………..

 

x^4 \; + \; y^3 \; = \; 67 \, z^2

515095^4 + 88440953007^3 = 67\times 3213236704795652^2

530645718049^4 + 93861626027912934788799^3
= 67\times 3513133949064917494371076204093240^2

546665912276384215^4 + 99614539881657133995715464767055407^3
= 67\times 3841021150429418875934440354547596060422860503124748^2
………………………………………………………..
 

x^4 \; + \; y^3 \; = \; 71 \, z^2

194399^4 + 12596990399^3 = 71\times 167791912167960^2
75581942401^4 + 1904210005702693881599^3 = 71\times 9861502516738650397382716144080^2

29386108041429599^4 + 287847781940857780979265224433599^3
= 71\times 579582356815423766314571960865963196125612983880^2
……………………………………………………….
 

x^4 \; + \; y^3 \; = \; 73 \, z^2

74^4 + 1824^3 = 73\times 9140^2
10951^4 + 39974799^3 = 73\times 29581354220^2
1620674^4 + 875528071424^3 = 73\times 95883456742437420^2
………………………………………………
 

x^4 \; + \; y^3 \; = \; 79 \, z^2

228151^4 + 17350959599^3 = 79\times 257141221316460^2

104105757601^4 + 3612669588559389758399^3
= 79\times 24430301074434611183285100562920^2

47503665404623351^4 + 752199408958136465960962058156399^3
= 79\times 2321057695948304241463556835801330247584889069380^2
…………………………………………………..
 

x^4 \; + \; y^3 \; = \; 83 \, z^2

8553815^4 + 24389250351407^3 = 83\times 13220827273491469236^2

146335502108449^4 + 7138026392443960574852395199^3
= \; 83\times 66195455951372376322612784624923547495640^2

2503453625935556812055^4 + 2089093352403295603646777815777504864441007^3
= \; 83\times 331434508443841217944204525142676360409953903860485730978049564^2
………………………………………………….

 

x^4 \; + \; y^3 \; = \; 89 \, z^2

2402^4 + 1923200^3 = 89\times 282710988^2
11539207^4 + 44384432729615^3 = 89\times 31343753780464182372^2

55434348026^4 + 1024322313689230032224^3
= \; 89\times 3475041111014794061990510317140^2
………………………………………………….

 

x^4 \; + \; y^3 \; = \; 97 \, z^2

290^4 + 28032^3 \; = \; 97\times 476612^2
168199^4 + 9430301199^3 \; = \; 97\times 92982769861580^2
97555130^4 + 3172334463105632^3 \; = \; 97\times 18141892397922638360988^2
………………………………………………..

 

 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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