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That is, if you say x (mod m) = 2, there are an infinite number of solutions. Say m
= 5; then some of the first possible values of x are 2, 7, 12, 17, etc. The list is
infinite.
But if x and m are both unique numbers, as in this question, there can only be one
result of x (mod m). Think of it this way: x (mod m) is just the remainder when
you divide x by m. Have you ever gotten more than one remainder when dividing
two numbers? I would hope not!
Here’s a final example to illustrate the point:
x = 17
m=7
Then x (mod m) = remainder of (17/7) = 3. The set of numbers from 0… m1 is
{0, 1, 2, 3, 4, 5, 6}, of which only one element is equal to 3....
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This document was uploaded on 02/26/2014 for the course ECE 490SIC at Drexel.
 Fall '08
 Trachtenberg

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