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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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re: A little research Comment 2 of 2 |
(In reply to A little research by Brian Smith)

Brian, a correction:

24^5 + 28^5 + 67^5 = 3^5 +54^5 + 62^5, which has a sum of the bases for each side of the equation equal to 119, for a total sum of 238.

The equation with the next smaller sum of the bases,
18^5 + 44^5 + 66^5 = 13^5 + 51^5 + 64^5
having the sum of the bases for each side of its equation equal to 128, for a total sum of 256 is correct.

  Posted by Dej Mar on 2015-12-21 20:36:29

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