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
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.