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.

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- Mar 19th 2008, 10:39 AMchriscmod
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. - Mar 19th 2008, 10:45 AMtopsquark
$\displaystyle x = 1 \text{ (mod 10)}$

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 $\displaystyle 1 \equiv 1 \text{ mod 10}$ 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 - Mar 19th 2008, 11:19 AMcolby2152
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