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1998 has same sum of digits in base b and 10 (Chile NMO 1989 P1)

Source:

November 19, 2021
number theorysum of digitsDigits

Problem Statement

Writing 19891989 in base bb, we obtain a three-digit number: xyzxyz. It is known that the sum of the digits is the same in base 1010 and in base bb, that is, 1+9+8+9=x+y+z1 + 9 + 8 + 9 = x + y + z. Determine x,y,z,b.x,y,z,b.
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