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Get the bases! (Posted on 2018-10-17) Difficulty: 3 of 5
The number 1987 can be written as a three digit number xyz in some base b.
If x + y + z = 1 + 9 + 8 + 7=25, determine all possible values of x, y, z, b.

Source: 1987 Canadian Mathematical Olympiad.

See The Solution Submitted by Ady TZIDON    
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re(2): computer soln Comment 5 of 5 |
(In reply to re: computer soln by Ady TZIDON)

Right. I had gotten as far as playing around with equations summing to 1962. I had not made the leap to factor-out b-1. xdog showed the way. Coming from science and engineering I am not so used to integer modern algebra per se. So, as a practice, I took on 2018 as xyz( base b) where the digits add to 17. (2 solution are to be found, not counting negative bases. 

And, hey, what about imaginary or complex bases?

Edited on October 19, 2018, 3:05 am
  Posted by Steven Lord on 2018-10-18 12:42:04

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