Modnotes-Arup - Notes about mod Arup Guha First we'll...

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Notes about mod Arup Guha First we’ll define divisibility. We say that a | b if and only if there is some integer c such that b = ac. In English, “a | b” would be read as “b is divisible by a.” For example, 6 | 18, 197 | 0 and 34 | 34. Now, let’s define mod: a ≡ b (mod n) if and only if n | (a – b). (This just means there exists some integer c such that a – b = nc.) In essence, this is true if n divides evenly into the difference of a and b. Alternatively, we can think of it as follows: when a and b are divided by n, they leave the same remainder. In our class, typically we will make some mathematical calculation and then we’d like to know what letter a particular number corresponds to. What we really want is give some integer a, we want to find a value b such that 0 ≤ b < 26 and a ≡ b (mod 26). For example, if we get 194 after some calculation and want to know what letter it is, our goal is to find the unique value of b such that 194 ≡ b (mod 26), with 0 ≤ b < 26 We can determine that 194 ≡ 12 (mod 26). We can verify this because 194 – 12 = 182 and 182 = 26x7. The easy way to find b when the starting value is greater than 26 is to
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This note was uploaded on 07/04/2011 for the course CIS 3360 taught by Professor Guha during the Fall '06 term at University of Central Florida.

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Modnotes-Arup - Notes about mod Arup Guha First we'll...

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