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MATH / In this problem, a and b are positive integers.

Problem

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problem

In this problem, aa and bb are positive integers. When aa is written in base 99, its last digit is 55. When bb is written in base 66, its last two digits are 5353. When a−ba-b is written in base 33, what are its last two digits? Assume a−ba-b is positive.
Plain-text mathematical notation (without MathML)
In this problem, a and b are positive integers.

When a is written in base 9, its last digit is 5.

When b is written in base 6, its last two digits are 53.

When a−b is written in base 3, what are its last two digits?  Assume a−b is positive.
Original LaTeX notation
In this problem, $a$ and $b$ are positive integers.

When $a$ is written in base $9$, its last digit is $5$.

When $b$ is written in base $6$, its last two digits are $53$.

When $a-b$ is written in base $3$, what are its last two digits?  Assume $a-b$ is positive.

level

Level 5

type

Number Theory

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Source and history

task_id
9e3dd017-ec77-5d88-8266-c08e72280834
task_key
number~5ftheory--test--9e3dd017-ec77-5d88-8266-c08e72280834
task_revision_id
1
config / split
number_theory / test

Official source

initial import