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No software allowed ! (Posted on 2017-05-07) Difficulty: 3 of 5
Find positive integers a, b, and c, all different, such that
a^3 + b^3 = c^4.

Please obey the title !

No Solution Yet Submitted by Ady TZIDON    
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New solutions not relatively prime | Comment 4 of 6 |
(In reply to re(2): Solution by Charlie)

I note that Charlie has several solutions that are not of the Brian Smith sort, in that a and b are not multiples of c.  So Brian's excellent method does not find all solutions.

The first of these are:

793 854 183    (gcd = 61)
737 1072 201  (gcd = 67)
730 1241 219  (gcd = 73)

They are not relatively prime.  I believe I have read someplace that solutions to this equation must have a gcd > 1.

  Posted by Steve Herman on 2017-05-07 18:41:17
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