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

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re: New solutions not relatively prime | Comment 5 of 6 |
(In reply to New solutions not relatively prime by Steve Herman)

I would have been shocked if my solution did find all possible solutions.  I had recently solved Taking the Fifth, in which Broll asks about a 'nontrivial' solution to a^3+b^3=c^5 (solutions where a,b,c are not based off of a solution to a'^3+b'^3=c'^2).

Now knowing 183, 201, 219 are nontrivial solutions for a^3+b^3=c^4, I went to the OEIS and found A051387 "Numbers whose 4th power is the sum of two positive cubes in a nontrivial way".

 Posted by Brian Smith on 2017-05-07 19:45:56

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