CONGRUENCES AND MODULAR ARITHMETIC. Congruence and Modular Arithmetic Definition: a is congruent to b mod n means that n∣a -b, (a-b) is divisible by n. Notation: a ≡ b (mod n) , a, b, n ∈ I, n ≠ b Ex . 42 ≡ 30 (mod 3)
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Congruence and Modular Arithmetic
Definition:a is congruent to b mod n means that n∣a-b, (a-b) is divisible by n.
Notation: a ≡ b (mod n), a, b, n ∈ I, n ≠ b
Ex. 42 ≡ 30 (mod 3)
Since, 3 ∣ 42 – 30
a ≡ b (mod n), it means that n ∣ a – b
Ex. 3 ≡ 4 (mod 5)
Proposition: Congruence mod m is an equivalent relation:
Equivalence relationis a reflexive(every element is in the relation to itself), symmetric(element a has the same relation to element b that b has to a), and transitive (a is in a given relation to b and b is in the same relation to c, then a is also in that relation to c) relationship between elements of a set.
Proposition: Any relation is called an equivalence relation if it satisfied the following properties:
EP 4/1 Group 3
Chosita K. “2”
Hsinju C. “3”
Nipawan P. “5”
Ob-Orm U. “11”
Mr. Wendel Glenn Jumalon