1. ## Modular Arithmetic

Hi Guys,

Having some trouble with basic modular arithmetic, most of the materials i have dont seem to be helping..

a simple question 2 mod 10 = 2.. how did they get = 2?

3 mod 18 = 3, could you please explain the process

2. Originally Posted by extatic
Hi Guys,

Having some trouble with basic modular arithmetic, most of the materials i have dont seem to be helping..

a simple question 2 mod 10 = 2.. how did they get = 2?

3 mod 18 = 3, could you please explain the process
Definition $\displaystyle a=b\!\!\pmod n\Longleftrightarrow n\mid (a-b)\Longrightarrow a-b=kn$ , when all the letters

here symbolize integer numbers.

Thus, $\displaystyle 2=2\!\!\pmod{10}$ because $\displaystyle 10\mid(2-2=0)\,,\,\,0=10\cdot 0$ , and etc.

A less trivial example: $\displaystyle 11=47\!\!\pmod{18}\,\,because\,\,11-47=-36=18\cdot (-2)$

Tonio

3. Originally Posted by tonio
Definition $\displaystyle a=b\!\!\pmod n\Longleftrightarrow n\mid (a-b)\Longrightarrow a-b=kn$ , when all the letters

here symbolize integer numbers.

Thus, $\displaystyle 2=2\!\!\pmod{10}$ because $\displaystyle 10\mid(2-2=0)\,,\,\,0=10\cdot 0$ , and etc.

A less trivial example: $\displaystyle 11=47\!\!\pmod{18}\,\,because\,\,11-47=-36=18\cdot (-2)$

Tonio
Thank you Tonio,

what if b (mod n) is only given, not a ??

4. Originally Posted by extatic
Thank you Tonio,

what if b (mod n) is only given, not a ??

$\displaystyle b\!\!\pmod n$ hasn't much meaning beyond indicating that we're considering an element b modulo some integer n...

Tonio

5. I'd like to add to tonio's reply. Programmers use b (mod n) to represent the remainder upon dividing b by n. For example, 7 (mod 5) equals 2, since 7/5 = 1, with remainder 2. See , for example, section 3.4 of Concrete Mathematics by Graham, Knuth and Patashnik.

6. Thank you to you both

Petek thank you for that..

7. If this helps anyone,

2648 (mod 7)

2648 / 7 = 378.28...........
378 x 7 = 2646

2648 - 2646 = 2

2468 (mod 7) = 2

thanks for the help guys