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Unformatted text preview: Integral domain: M5) Multiplicative Identity a1= 1a = a M6) No zero divisors, if ab = 0 either a=0 or b=0 Fields: M7) Multiplicative Inverse Mod arithmetic A residue is in range from 0 to n-1 Two values are congruent regardless of whether they are in range or not. Basic rules of divisibility: if a | 1, a = 1 or -1 if a | b and b | a, a = b or a=-b if b!= 0 then b | 0 if b|g and b|h, then b|(gx+hy) if a b (mod n) then f(a) f(b) (mod n), where f is a poly function with integer coefficients Example: 11 7 mod 13 Residue classes: , , etc. Example of finite field of size 7 Poly arithmetic with coefficients in Z p ....
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- Summer '09