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Quintic Power Query (Posted on 2015-12-21) Difficulty: 3 of 5
Each of A,B,C,D,E and F are distinct positive integers such that:

A5 + B5 + C5 = D5 + E5 + F5

Find the smallest value of A+B+C+D+E+F

No Solution Yet Submitted by K Sengupta    
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Some Thoughts A little research | Comment 1 of 2
Halfway down the page, the Mathworld page 
http://mathworld.wolfram.com/DiophantineEquation5thPowers.html lists 6 solutions, the smallest two being: 
24^5 + 28^5 + 27^5 = 3^5 + 54^5 + 62^5
18^5 + 44^5 + 66^5 = 13^5 + 51^5 + 64^5
The sum of the bases are 198 and 256, respectively.

  Posted by Brian Smith on 2015-12-21 11:49:11
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