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Binary Number Theory-like problem

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    I have a function [itex] f: \mathbb Z_p \times \mathbb Z_p \to \mathbb Z_p [/itex] for some prime p. I am given [itex] (r_1, r_2) \in \mathbb Z_p \times \mathbb Z_p\setminus_{\left\{0,0\right\} } [/itex], and told that

    [itex] f(a_1, a_2) = f(b_1,b_2) \Leftrightarrow (a_1,a_2)-(b_1,b_2) = m (r_1,r_2) [/itex]
    for some integer m. That is, their difference is an integer multiple of [itex] (r_1, r_2) [/itex]. I need to find some way of converting this statement into binary, specifically something using XOR.

    3. The attempt at a solution
    I've been trying different things, such as [itex] f(a_1,a_2) = f(b_1,b_2) \Leftrightarrow (a_1,a_2) \oplus (b_1,b_2) = (r_1,r_2) [/itex] but I'm not even sure how to check if this is correct. Any ideas?
     
  2. jcsd
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