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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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computers not needed | Comment 3 of 5 |
Subtract the equations:


The first solution is b-1=18 which leads to 20x+y=109 and (x,y,z,b)=(5,9,B,19).  5*19*19+9*19+11=1987 and 5+9+11=25.

The second solution is sneakier.  If b-1=-18, -16x+y=-109 and (x,y,z,b)=(7,3,F,-17).  7*-17*-17+3*-17+15=1987 and 7+3+15=25.

  Posted by xdog on 2018-10-17 18:12:16
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