x^3 + y^3 = 13(z^3) and x^3 + y^3 = 31(z^3)

 

 

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

 
7^3 \; + \; 2^3 \; = \; 13 \; \times \; (3)^3

2513^3 \; + \; (-1388)^3 \; = \; 13 \; \times \; (1005)^3

26441619018689^3 \; + \; 40343602894936^3 \; = \; 13 \; \times \; (18636783082845)^3

 

 

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

 
137^3 \; + \; (-65)^3 \; = \; 31 \; \times \; (42)^3

277028111^3 \; + \; 316425265^3 \; = \; 31 \; \times \; (119531076)^3

 

                             ———————————————        

 

(40208)^3 \; + \; (-22208)^3 \; = \; 13 \; \times \; (16080)^3

(203553)^3 \; + \; (-112428)^3 \;  = \; 13 \; \times \; (81405)^3

(643328)^3 \; + \; (-355328)^3 \; = \; 13 \; \times \; (257280)^3

(2643958359322525696)^3 \; + \; (1732877944008802304)^3
= \; 13 \; \times \; (1221380216117329920)^3

(113565888938560867794944)^3 \; + \; (173274455036561044013056)^3
= \; 13 \; \times \; (80044373843465333637120)^3

 
 
 

Find other solutions
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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2 Responses to x^3 + y^3 = 13(z^3) and x^3 + y^3 = 31(z^3)

  1. paul says:

    Here are a few of type x^3 + y^3 = 13 z^3.
    Format is {x, y, z}

    {2,7,3}
    {4,14,6}
    {6,21,9}
    {8,28,12}
    {10,35,15}
    {12,42,18}
    {14,49,21}
    {16,56,24}
    {18,63,27}
    {20,70,30}
    {22,77,33}
    {24,84,36}
    {26,91,39}
    {28,98,42}

    Paul.

    • benvitalis says:

      (7, 2, 3) is a primitive solution

      (4, 14, 6) = 2 x [7, 2, 3 ]
      (21, 6, 9) = 3 x [7, 2, 3 ]

      (28, 8, 12) = 4 x [7, 2, 3 ]

      (35, 10, 15) = 5 x [7, 2, 3]
      (42, 12, 18) = 6 x [7, 2, 3 ]
      (49, 14, 21) = 7 x [7, 2, 3 ]
      (56, 16, 24) = 8 x [7, 2, 3 ]
      (63, 18, 27) = 9 x [7, 2, 3 ]
      (70, 20, 30) = 10 x [7, 2, 3 ]
      (77, 22, 33) = 11 x [7, 2, 3 ]
      (84, 24, 36) = 12 x [7, 2, 3 ]
      (91, 26, 39) = 13 x [7, 2, 3 ]
      (98, 28, 42) = 14 x [7, 2, 3 ]

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