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MATH / A base-10 integer n can be represented as 32_(a) in one base and 23_(b) in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?

Problem

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problem

A base-10 integer nn can be represented as 32a32_a in one base and 23b23_b in another base, where aa and bb are any integer bases larger than 3. What is the smallest possible sum aa+bb?
Plain-text mathematical notation (without MathML)
A base-10 integer n can be represented as 32_(a) in one base and 23_(b) in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?
Original LaTeX notation
A base-10 integer $n$ can be represented as $32_a$ in one base and $23_b$ in another base, where $a$ and $b$ are any integer bases larger than 3. What is the smallest possible sum $a$+$b$?

level

Level 4

type

Number Theory

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Source and history

task_id
267c44cf-5389-5336-bbb3-22a7c5dd817d
task_key
number~5ftheory--test--267c44cf-5389-5336-bbb3-22a7c5dd817d
task_revision_id
1
config / split
number_theory / test

Official source

initial import