N^3 = A^3 + B^3 + C^3

 
 

N^3 \; = \; A^3 \; + \; B^3 \; + \; C^3,        N \leq 1000

A, B, C   are distinct positive integers
 

18^3 \; = \; 9^3 \; + \; 12^3 \; + \; 15^3
84^3 \; = \; 28^3 \; + \; 53^3 \; + \; 75^3

105^3 \; = \; 33^3 \; + \; 70^3 \; + \; 92^3

260^3 \; = \; 65^3 \; + \; 127^3 \; + \; 248^3
288^3 \; = \; 144^3 \; + \; 192^3 \; + \; 240^3

458^3 \; = \; 19^3 \; + \; 362^3 \; + \; 365^3
488^3 \; = \; 76^3 \; + \; 368^3 \; + \; 404^3

522^3 \; = \; 135^3 \; + \; 378^3 \; + \; 441^3
560^3 \; = \; 196^3 \; + \; 392^3 \; + \; 476^3

602^3 \; = \; 259^3 \; + \; 410^3 \; + \; 509^3
630^3 \; = \; 126^3 \; + \; 249^3 \; + \; 615^3
648^3 \; = \; 324^3 \; + \; 432^3 \; + \; 540^3
665^3 \; = \; 266^3 \; + \; 545^3 \; + \; 484^3
698^3 \; = \; 391^3 \; + \; 458^3 \; + \; 569^3

752^3 \; = \; 460^3 \; + \; 488^3 \; + \; 596^3

810^3 \; = \; 531^3 \; + \; 522^3 \; + \; 621^3
872^3 \; = \; 604^3 \; + \; 560^3 \; + \; 644^3

938^3 \; = \; 679^3 \; + \; 602^3 \; + \; 665^3

 

Find other solutions
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

One Response to N^3 = A^3 + B^3 + C^3

  1. paul says:

    Here are the solutions with N<=100

    6^3 = 3^3 + 4^3 + 5^3

    9^3 = 1^3 + 6^3 + 8^3

    12^3 = 6^3 + 8^3 + 10^3

    18^3 = 2^3 + 12^3 + 16^3
    18^3 = 9^3 + 12^3 + 15^3

    19^3 = 3^3 + 10^3 + 18^3

    20^3 = 7^3 + 14^3 + 17^3

    24^3 = 12^3 + 16^3 + 20^3

    25^3 = 4^3 + 17^3 + 22^3

    27^3 = 3^3 + 18^3 + 24^3

    28^3 = 18^3 + 19^3 + 21^3

    29^3 = 11^3 + 15^3 + 27^3

    30^3 = 15^3 + 20^3 + 25^3

    36^3 = 4^3 + 24^3 + 32^3
    36^3 = 18^3 + 24^3 + 30^3

    38^3 = 6^3 + 20^3 + 36^3

    40^3 = 14^3 + 28^3 + 34^3

    41^3 = 2^3 + 17^3 + 40^3
    41^3 = 6^3 + 32^3 + 33^3

    42^3 = 21^3 + 28^3 + 35^3

    44^3 = 16^3 + 23^3 + 41^3

    45^3 = 5^3 + 30^3 + 40^3

    46^3 = 3^3 + 36^3 + 37^3
    46^3 = 27^3 + 30^3 + 37^3

    48^3 = 24^3 + 32^3 + 40^3

    50^3 = 8^3 + 34^3 + 44^3

    53^3 = 29^3 + 34^3 + 44^3

    54^3 = 6^3 + 36^3 + 48^3
    54^3 = 12^3 + 19^3 + 53^3
    54^3 = 27^3 + 36^3 + 45^3

    56^3 = 36^3 + 38^3 + 42^3

    57^3 = 9^3 + 30^3 + 54^3

    58^3 = 15^3 + 42^3 + 49^3
    58^3 = 22^3 + 30^3 + 54^3

    60^3 = 21^3 + 42^3 + 51^3
    60^3 = 30^3 + 40^3 + 50^3

    63^3 = 7^3 + 42^3 + 56^3

    66^3 = 33^3 + 44^3 + 55^3

    67^3 = 22^3 + 51^3 + 54^3

    69^3 = 36^3 + 38^3 + 61^3

    70^3 = 7^3 + 54^3 + 57^3

    71^3 = 14^3 + 23^3 + 70^3

    72^3 = 8^3 + 48^3 + 64^3
    72^3 = 34^3 + 39^3 + 65^3
    72^3 = 36^3 + 48^3 + 60^3

    75^3 = 12^3 + 51^3 + 66^3
    75^3 = 38^3 + 43^3 + 66^3

    76^3 = 12^3 + 40^3 + 72^3
    76^3 = 31^3 + 33^3 + 72^3

    78^3 = 39^3 + 52^3 + 65^3

    80^3 = 28^3 + 56^3 + 68^3

    81^3 = 9^3 + 54^3 + 72^3
    81^3 = 25^3 + 48^3 + 74^3

    82^3 = 4^3 + 34^3 + 80^3
    82^3 = 12^3 + 64^3 + 66^3
    82^3 = 19^3 + 60^3 + 69^3

    84^3 = 28^3 + 53^3 + 75^3
    84^3 = 42^3 + 56^3 + 70^3
    84^3 = 54^3 + 57^3 + 63^3

    85^3 = 50^3 + 61^3 + 64^3

    87^3 = 20^3 + 54^3 + 79^3
    87^3 = 26^3 + 55^3 + 78^3
    87^3 = 33^3 + 45^3 + 81^3
    87^3 = 38^3 + 48^3 + 79^3

    88^3 = 21^3 + 43^3 + 84^3
    88^3 = 25^3 + 31^3 + 86^3
    88^3 = 32^3 + 46^3 + 82^3

    89^3 = 17^3 + 40^3 + 86^3

    90^3 = 10^3 + 60^3 + 80^3
    90^3 = 25^3 + 38^3 + 87^3
    90^3 = 45^3 + 60^3 + 75^3
    90^3 = 58^3 + 59^3 + 69^3

    92^3 = 6^3 + 72^3 + 74^3
    92^3 = 54^3 + 60^3 + 74^3

    93^3 = 32^3 + 54^3 + 85^3

    95^3 = 15^3 + 50^3 + 90^3

    96^3 = 19^3 + 53^3 + 90^3
    96^3 = 48^3 + 64^3 + 80^3

    97^3 = 45^3 + 69^3 + 79^3

    99^3 = 11^3 + 66^3 + 88^3

    100^3 = 16^3 + 68^3 + 88^3
    100^3 = 35^3 + 70^3 + 85^3

    Paul.

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