Equation : x^2 + y^3 = z^4

 
 

x^2 \; + \; y^3 \; = \; z^4
 

28^2 \; + \; 8^3 \; = \; 6^4

41328^2 \; + \; 288^3 \; = \; 204^4

48015100^2 \; + \; 9800^3 \; = \; 6930^4

55420360128^2 \; + \; 332928^3 \; = \; 235416^4

63955420452028^2 \; + \; 11309768^3 \; = \; 7997214^4

73804512448220400^2 \; + \; 384199200^3 \; = \; 271669860^4

85170343840128993628^2 \; + \; 13051463048^3 \; = \; 9228778026^4

98286503001614049040128^2 \; + \; 443365544448^3 \; = \; 313506783024^4

113422539294015341873095900^2 \; + \; 15061377048200^3 \; = \; 10650001844790^4

130889512058807571649797612528^2 \; + \; 511643454094368^3 \; = \; 361786555939836^4

 

Determine the next values.

Establish the recurrence relation.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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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 Equation : x^2 + y^3 = z^4

  1. paul says:

    The next values are

    151046383493325216709193157453628^2 + 17380816062160328^3 = 12290092900109634^4

    The recurrences are for the square, cube and 4th power

    {1189,-40426,40426,-1189,1}
    {35,-35,1}
    {35,-35,1}

    Paul.

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