Equal sums of 5-th powers (4 terms)

 
 
Here are a few with the terms less than 100

  0^5 + 2^5 + 37^5 + 50^5 = 9^5 + 11^5 + 17^5 + 52^5 = 381843989
  0^5 + 3^5 + 22^5 + 25^5 = 1^5 + 8^5 + 14^5 + 27^5 = 14919500
  1^5 + 10^5 + 27^5 + 32^5 = 8^5 + 9^5 + 19^5 + 34^5 = 48003340
  1^5 + 13^5 + 17^5 + 23^5 = 3^5 + 9^5 + 21^5 + 21^5 = 8227494
  3^5 + 38^5 + 41^5 + 56^5 = 13^5 + 31^5 + 36^5 + 58^5 = 745823388
  3^5 + 41^5 + 42^5 + 54^5 = 9^5 + 35^5 + 40^5 + 56^5 = 705712700
  4^5 + 11^5 + 13^5 + 22^5 = 5^5 + 6^5 + 19^5 + 20^5 = 5687000
  4^5 + 13^5 + 26^5 + 31^5 = 11^5 + 14^5 + 16^5 + 33^5 = 40882844
  5^5 + 20^5 + 21^5 + 24^5 = 9^5 + 17^5 + 18^5 + 26^5 = 15249850
  6^5 + 43^5 + 49^5 + 54^5 = 8^5 + 39^5 + 52^5 + 53^5 = 888656492
  7^5 + 14^5 + 33^5 + 36^5 = 11^5 + 12^5 + 29^5 + 38^5 = 100156200
  7^5 + 16^5 + 72^5 + 89^5 = 9^5 + 12^5 + 76^5 + 87^5 = 7520042464
  7^5 + 21^5 + 23^5 + 33^5 = 11^5 + 13^5 + 29^5 + 31^5 = 49672644
  7^5 + 32^5 + 36^5 + 41^5 = 9^5 + 28^5 + 39^5 + 40^5 = 209893616
  7^5 + 34^5 + 43^5 + 56^5 = 15^5 + 32^5 + 35^5 + 58^5 = 743192450
  8^5 + 23^5 + 42^5 + 57^5 = 21^5 + 24^5 + 26^5 + 59^5 = 738852400
  9^5 + 40^5 + 51^5 + 60^5 = 13^5 + 38^5 + 47^5 + 62^5 = 1225084300

12^5 + 21^5 + 23^5 + 38^5 = 13^5 + 14^5 + 31^5 + 36^5 = 90004444
12^5 + 32^5 + 36^5 + 48^5 = 14^5 + 26^5 + 42^5 + 46^5 = 349073408
13^5 + 39^5 + 59^5 + 71^5 = 15^5 + 35^5 + 63^5 + 69^5 = 2609749142
14^5 + 30^5 + 45^5 + 35^5 = 10^5 + 34^5 + 37^5 + 43^5 = 261887824
14^5 + 33^5 + 37^5 + 66^5 = 16^5 + 21^5 + 49^5 + 64^5 = 1361349750
16^5 + 29^5 + 41^5 + 74^5 = 17^5 + 18^5 + 53^5 + 72^5 = 2356422550
17^5 + 24^5 + 33^5 + 36^5 = 21^5 + 22^5 + 29^5 + 38^5 = 108984050
19^5 + 34^5 + 37^5 + 46^5 = 27^5 + 29^5 + 32^5 + 48^5 = 323218456

 
 
Find other solutions
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to Equal sums of 5-th powers (4 terms)

  1. Paul says:

    There are 1909 solutions (not all different) with a < b < c < d <=100, here are the first 5 and last 2 that are different terms. format is

    {{a, b, c, d, etc},{e, f, g, h, etc}}

    {{1,3,9,55,503343668},{15,22,38,53,503343668}}
    {{1,3,28,53,435406105},{4,25,34,52,435406105}}
    {{1,3,30,79,3101356643},{18,51,64,70,3101356643}}
    {{1,3,52,91,6620525727},{8,16,31,92,6620525727}}
    {{1,3,74,94,9558047092},{16,24,33,99,9558047092}}

    ….
    {{53,79,85,91,14172626468},{60,68,87,93,14172626468}}
    {{54,74,89,93,15219114790},{61,67,85,97,15219114790}}

    Paul.

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