http://img91.imageshack.us/img91/7874/61804661.jpg

$\displaystyle \frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}$

Im not sure how to multiply this out please show steps on how to do this. Thanks

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- Mar 2nd 2009, 06:26 PMronaldo_07[SOLVED] Z18 Calculation
http://img91.imageshack.us/img91/7874/61804661.jpg

$\displaystyle \frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}$

Im not sure how to multiply this out please show steps on how to do this. Thanks - Mar 2nd 2009, 06:56 PMTheEmptySet
- Mar 3rd 2009, 03:22 AMronaldo_07
How did you get from 75 to 3mod(17)?

- Mar 3rd 2009, 07:01 AMrajr
Hi as you mentioned it's not 3 mod 17, actually it is 3 mod 18.

take 75 and when you try to divide 75 by 18, you will get 3 as a remainder and hence 3 mod 18. is it helpful...? :) - Mar 3rd 2009, 09:32 AMThePerfectHacker
Here is another way. To find inverse of 7 you need to solve $\displaystyle 7x\equiv 1(\bmod 18)$.

This is equivalent to $\displaystyle 7x\equiv 1 - 2\cdot 18(\bmod 18)\implies 7x\equiv -35(\bmod 18) \implies $$\displaystyle x\equiv -5(\bmod 18)\implies x\equiv 13(\bmod 18)$.