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Base Systems: (Proof track.) Give a complete justification. Find largest base in which math.

Convert and compute in bases.

Try the problem

**(Proof track.)** Give a complete justification. Find largest base in which (123)b<200(123)_b<200.

Hint and answer

Concept to use

Digit DP style.

Hint

Expand the numeral as a polynomial in its base and enforce valid-digit constraints.

Answer

12

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