1. ## Modular Arithmatic

Find the value of x:

(35-207)= x mod 11

Can someone show the steps for this answer? I just don't know what to do after I get -172.

2. Originally Posted by nippy
Find the value of x:

(35-207)= x mod 11

Can someone show the steps for this answer? I just don't know what to do after I get -172.
$(35 - 207) \equiv x~\text{mod 11}$

$-172 \equiv x~\text{mod 11}$

So x is the remainder when you divide -172 by 11, ie. it is the solution of the equation:
$-172 = 11 \cdot n + x$
where n is an integer and x is defined to be $0 \leq x < 11$.

I get n = -16 as giving x in the required interval, so
$4 \equiv x~\text{mod 11}$

-Dan