A^4 + B^4 + C^4 + D^4 = N^2

 
 
4375^4 + 9000^4 + 12000^4 + 8088^4 = 178724881^2

3398759^4 + 1318200^4 + 3163680^4 + 2563320^4 = 16727475700081^2

13446881^4 + 9432960^4 + 17686800^4 + 13133040^4 = 410145497588161^2

205859375^4 + 36750000^4 +126000000^4 + 112283472^4 = 46997066691015841^2

28998521^4 + 409735200^4 + 430221960^4 + 297764040^4 = 265151359688347441^2

2025968041^4+510582240^4+1489198200^4+1277943240^4 = 4949813081178337681^2

4292330959^4+446608080^4+1984924800^4+1847923920^4 = 19148667486258019681^2

9792086921^4+10504761120^4+16882651800^4+11882508120^4 = 350064905034860220241^2

48169680839^4+3295764120^4+17976895200^4+17126526120^4 = 2361031077358543903921^2

66279370625^4+8858304000^4+34879572000^4+31890089952^4 = 4671031225959061528321^2

36540229375^4+33495462000^4+56840784000^4+40731461232^4 = 4028957129011793932801^2

20475131761^4+98592468480^4+112970536800^4+76343736480^4 = 17073681946762575921121^2

359505704375^4+17436237000^4+112664916000^4+108797482248^4 = 130404864992668244007121^2

241845495625^4+122569524000^4+262162593000^4+204200250408^4 = 100544014869482214974161^2

306119393839^4+171561255840^4+351920524800^4+270026271840^4 = 174076216081452563317921^2

84899580479^4+555270253200^4+615068588160^4+418621142160^4 = 518598700332095070829441^2

 

Can you find smaller values?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to A^4 + B^4 + C^4 + D^4 = N^2

  1. paul says:

    These are those with a < b < c < d < 50

    1^4 + 2^4 + 24^4 + 46^4 = 2193^2
    1^4 + 9^4 + 31^4 + 41^4 = 1938^2
    1^4 + 11^4 + 17^4 + 19^4 = 478^2
    1^4 + 13^4 + 27^4 + 31^4 = 1218^2
    2^4 + 4^4 + 6^4 + 7^4 = 63^2
    2^4 + 4^4 + 7^4 + 12^4 = 153^2
    2^4 + 4^4 + 8^4 + 19^4 = 367^2
    2^4 + 4^4 + 13^4 + 26^4 = 697^2
    2^4 + 8^4 + 11^4 + 22^4 = 503^2
    2^4 + 13^4 + 44^4 + 46^4 = 2873^2
    2^4 + 14^4 + 16^4 + 17^4 = 433^2
    2^4 + 18^4 + 22^4 + 29^4 = 1023^2
    2^4 + 22^4 + 34^4 + 38^4 = 1912^2
    2^4 + 22^4 + 46^4 + 47^4 = 3097^2
    2^4 + 34^4 + 41^4 + 42^4 = 2697^2
    2^4 + 36^4 + 38^4 + 49^4 = 3087^2
    3^4 + 4^4 + 8^4 + 14^4 = 207^2
    3^4 + 7^4 + 29^4 + 31^4 = 1278^2
    3^4 + 14^4 + 24^4 + 48^4 = 2383^2
    3^4 + 17^4 + 27^4 + 33^4 = 1342^2
    4^4 + 6^4 + 9^4 + 24^4 = 583^2
    4^4 + 7^4 + 22^4 + 26^4 = 833^2
    4^4 + 8^4 + 12^4 + 14^4 = 252^2
    4^4 + 8^4 + 14^4 + 24^4 = 612^2
    4^4 + 8^4 + 14^4 + 31^4 = 983^2
    4^4 + 8^4 + 16^4 + 38^4 = 1468^2
    4^4 + 8^4 + 23^4 + 34^4 = 1273^2
    4^4 + 8^4 + 34^4 + 37^4 = 1793^2
    4^4 + 16^4 + 22^4 + 44^4 = 2012^2
    4^4 + 18^4 + 21^4 + 42^4 = 1847^2
    4^4 + 28^4 + 32^4 + 34^4 = 1732^2
    6^4 + 8^4 + 16^4 + 17^4 = 393^2
    6^4 + 8^4 + 16^4 + 28^4 = 828^2
    6^4 + 11^4 + 12^4 + 24^4 = 607^2
    6^4 + 12^4 + 18^4 + 21^4 = 567^2
    6^4 + 12^4 + 21^4 + 36^4 = 1377^2
    6^4 + 17^4 + 18^4 + 42^4 = 1817^2
    7^4 + 21^4 + 41^4 + 43^4 = 2538^2
    8^4 + 12^4 + 13^4 + 14^4 = 303^2
    8^4 + 12^4 + 16^4 + 17^4 = 417^2
    8^4 + 12^4 + 18^4 + 48^4 = 2332^2
    8^4 + 12^4 + 46^4 + 47^4 = 3063^2
    8^4 + 14^4 + 17^4 + 38^4 = 1487^2
    8^4 + 16^4 + 17^4 + 48^4 = 2337^2
    8^4 + 16^4 + 24^4 + 28^4 = 1008^2
    8^4 + 16^4 + 28^4 + 48^4 = 2448^2
    8^4 + 23^4 + 32^4 + 48^4 = 2577^2
    9^4 + 12^4 + 24^4 + 42^4 = 1863^2
    10^4 + 20^4 + 30^4 + 35^4 = 1575^2
    10^4 + 20^4 + 32^4 + 35^4 = 1649^2
    9^4 + 12^4 + 24^4 + 42^4 = 1863^2
    12^4 + 16^4 + 32^4 + 34^4 = 1572^2
    12^4 + 18^4 + 21^4 + 44^4 = 2017^2
    12^4 + 22^4 + 24^4 + 39^4 = 1703^2
    12^4 + 22^4 + 24^4 + 48^4 = 2428^2
    12^4 + 24^4 + 36^4 + 42^4 = 2268^2
    6^4 + 12^4 + 21^4 + 36^4 = 1377^2
    2^4 + 36^4 + 38^4 + 49^4 = 3087^2
    16^4 + 21^4 + 22^4 + 34^4 = 1353^2
    16^4 + 21^4 + 44^4 + 46^4 = 2913^2
    16^4 + 24^4 + 26^4 + 28^4 = 1212^2
    16^4 + 24^4 + 32^4 + 34^4 = 1668^2
    16^4 + 29^4 + 32^4 + 34^4 = 1777^2
    16^4 + 32^4 + 34^4 + 41^4 = 2297^2
    16^4 + 18^4 + 23^4 + 56^4 = 3207^2
    17^4 + 19^4 + 23^4 + 43^4 = 1978^2
    3^4 + 9^4 + 41^4 + 51^4 = 3098^2
    24^4 + 33^4 + 34^4 + 48^4 = 2857^2
    24^4 + 36^4 + 39^4 + 42^4 = 2727^2
    27^4 + 34^4 + 44^4 + 46^4 = 3177^2
    28^4 + 32^4 + 34^4 + 47^4 = 2807^2

    Paul.

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