Math Problem Statement

the number n can be written as abc in base 6, can be written in base 9 as cba, find the base 10 representation of n

Solution

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Math Problem Analysis

Mathematical Concepts

Number Systems
Base Conversion
Algebra
Modular Arithmetic

Formulas

n = 36a + 6b + c (base 6 representation)
n = 81c + 9b + a (base 9 representation)
35a = 3b + 80c

Theorems

Divisibility Rules
Positional Notation in Number Systems

Suitable Grade Level

Grades 10-12