The denition of congruence gives a rmod n denition 6

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Unformatted text preview: r < n, such that a = qn + r. The definition of congruence gives a ≡ r(mod n). Definition 6. If a, b ∈ Z and a ≡ b(mod n) we say that a is a residue of b modulo n. Remark 4. The above examples tells us that modulo n any integer a is congruent to one of 0, 1, 2, . . . , n − 1. These integers are called the least nonnegative residues modulo n. Definition 7. The set of integers {a0 , a1 , . . . , an−1 } is called a complete residue system modulo n provided (i) ai ￿≡ aj (mod n), whenever i ￿= j (ii) fo...
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This note was uploaded on 02/09/2013 for the course PMATH 340 taught by Professor W.alabama during the Spring '09 term at Waterloo.

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