1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find the remainder of the equation

  1. Jan 24, 2007 #1
    The task is to find the remainder of the equation:

    Now I know that if
    [tex]a \equiv b\ (mod\ m),\ c \equiv d\ (mod\ m) \Rightarrow[/tex]
    [tex]a + c \equiv b +d\ (mod\ m)[/tex] and [tex]ac \equiv bd\ (mod\ m)[/tex]


    [tex]18^2 \equiv b\ (mod\ 11) \Rightarrow \frac{18^2}{11}=29.454545... \Rightarrow b=18^2-11\cdot 29=5[/tex]
    and d<6 as the remainder b+d < 11.

    But as 2^100 is so large, I can't find d the way I found b. How to find it, or is there some other more convenient way that doesn't involve separating 18^2 and 2^100?
  2. jcsd
  3. Jan 24, 2007 #2


    User Avatar
    Homework Helper

    have you tried using this [tex]a\equiv b (\text{mod}\; m) \Rightarrow a^k\equiv b^k (\text{mod}\; m)[/tex] to help?

    The answer should be obvious after the use of this theorem
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook