[PDF] Congruences and Modular Arithmetic

3 Congruence

Definition 3.1 If a and b are integers and n > 0 we write a ? b mod n to mean n

Congruence and Congruence Classes

The next definition yields another example of an equivalence relation. Definition 11.2. Let a b

Congruences and Modular Arithmetic

Then congruence modulo n is an equivalence relation on Z. Proof (Sketch). Let ab

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Problem Set 4 Solutions

22-Feb-2005 Solution. The statement a ? b (mod n) implies n (a ? b) which means there is an integer k such that nk = ...

IIT Kharagpur 1 Basic Properties of Integers II

In other words a is congruent to b modulo n

1 p. 61 #26 Prove that the congruence ax = b (mod n) has a solution

and only if d = (a n) divides b. If d b

Congruences

Suppose n is a fixed integer. We will say that two integers a and b are congruent modulo n and we write a ? b mod n if a ? b is divisible by n.

BASIC PROPERTIES OF CONGRUENCES The letters a b

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Number Theory and Graph Theory Chapter 2 Prime numbers and

Let n be a positive integer and ab ? Z. Then a and b are said to be congruent modulo n or a is said to be congruent to b modulo n

1 Congruence and modular arithmetics

Let a b