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Even or Odd in Base 5?

```
Date: 09/23/1999 at 14:04:23
From: Susan
Subject: Different Number Bases

Could you describe a rule for determining whether a number written in
the base five number system is even or odd, without converting it to
base ten?
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```
Date: 09/23/1999 at 14:53:04
From: Doctor Mitteldorf
Subject: Re: Different Number Bases

Do you know how casting out nines works in base 10? You can add up the
digits of any number, and the number is divisible by nine if and only
if the sum of the digits is divisible by nine.

The same kind of thing works with base 5, where you "cast out fours."
The number is divisible by 4 if and only if the sum of the digits is
divisible by 4.

You can make things a little easier yet and derive with very similar
reasoning a rule that says: If a number in base 5 has an even number
of odd digits, then it is divisible by 2, but if it has an odd number
of odd digits, it is not.

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

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