Number theory, converting numbers too different bases

In summary, number theory is a branch of mathematics that studies patterns and relationships between whole numbers. Base conversion is the process of converting a number from one base system to another, often used for ease of working with or comparing numbers. Different bases are used for different purposes and some have unique properties for specific calculations. To convert a number to a different base, it is divided by the base and the remainders are taken in reverse order to form the new number. The most commonly used base system is decimal (base 10) in everyday life for counting and arithmetic.
  • #1
SNOOTCHIEBOOCHEE
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0

Homework Statement



Show that for any fixed a and b, there is an algorithm to convert an n-digit number from
base a to base b with O(n^2) operations.

The Attempt at a Solution



Really i am completley lost here. Working backwards, i know to convert from base a to a base b you must use the division algorithm, which requires something on the order of (n^2) operations, but i really don't know how to show any of this.
 
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Any thoughts?
 

1. What is number theory?

Number theory is a branch of mathematics that deals with the properties of numbers, particularly whole numbers. It involves studying patterns and relationships between numbers, as well as their properties and operations.

2. What is base conversion?

Base conversion is the process of converting a number from one base system to another. This is often done to make numbers easier to work with or to compare numbers from different systems.

3. Why do we use different bases?

Different base systems are used for different purposes. For example, the decimal system (base 10) is commonly used in everyday life, while the binary system (base 2) is used in computer programming. Some bases also have unique properties that make them useful for certain calculations.

4. How do you convert a number to a different base?

The process of converting a number to a different base involves dividing the number by the base repeatedly and keeping track of the remainders. The remainders, read from bottom to top, will give you the converted number in the new base.

5. What is the most commonly used base system?

The most commonly used base system is the decimal system (base 10), which uses the digits 0-9. This is the system we use in everyday life for counting and performing arithmetic operations.

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