# mod

• March 19th 2008, 10:39 AM
chrisc
mod
hi
are the following 2 things the same?

1 mod 10
1 (mod 10)

because i thought 1 mod 10 would equal 1
but going through some euler theorem examples, there are answers such that a large number can equal 1 (mod n), n being any number.
• March 19th 2008, 10:45 AM
topsquark
Quote:

Originally Posted by chrisc
hi
are the following 2 things the same?

1 mod 10
1 (mod 10)

because i thought 1 mod 10 would equal 1
but going through some euler theorem examples, there are answers such that a large number can equal 1 (mod n), n being any number.

$x = 1 \text{ (mod 10)}$
means that we have a number x, such that when it is divided by 10 it leaves a remainder of 1. 11, 21, 31, etc. are numbers of this type.

So whereas $1 \equiv 1 \text{ mod 10}$ so does 11. So there is a distinct difference between saying "1" and "1 (mod 10)." As far as the (mod 10) vs. mod 10, as far as I know there is no difference.

-Dan
• March 19th 2008, 11:19 AM
colby2152
1 mod(10) can equal 1, but also any number that when divided by a multiple of 10 gives a remainder of 1 such as 11, 21, 31, 41, 51, 61, 71, ....

Basically 1 mod(10) = 1 + 10n