# Can 5 odd numbers be added to get 30?

##### 2 Answers

No.

#### Explanation:

The sum of an odd number of odd numbers is odd.

Every odd number can be written as

For this question in particular, if we add:

We get:

# = 2((i+j+k+l+m+2) +1#

which is of the form

In normal integer arithmetic - no.

In modular arithmetic - yes with any odd modulo > 30.

#### Explanation:

**Normal arithmetic**

Suppose your

where

Then:

which is odd.

**Arithmetic modulo #31#**

Let

Then

In fact in modular arithmetic modulo an odd base all numbers are both odd and even.