Find the value of x:

(35-207)=xmod11

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

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- Jan 31st 2008, 03:45 PMnippyModular 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. - Jan 31st 2008, 05:00 PMtopsquark
$\displaystyle (35 - 207) \equiv x~\text{mod 11}$

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

So x is the remainder when you divide -172 by 11, ie. it is the solution of the equation:

$\displaystyle -172 = 11 \cdot n + x$

where n is an integer and x is defined to be $\displaystyle 0 \leq x < 11$.

I get n = -16 as giving x in the required interval, so

$\displaystyle 4 \equiv x~\text{mod 11}$

-Dan