Definition 3.1 If a and b are integers and n > 0 we write a ? b mod n to mean n
The next definition yields another example of an equivalence relation. Definition 11.2. Let a b
Then congruence modulo n is an equivalence relation on Z. Proof (Sketch). Let ab
22-Feb-2005 Solution. The statement a ? b (mod n) implies n (a ? b) which means there is an integer k such that nk = ...
In other words a is congruent to b modulo n
and only if d = (a n) divides b. If d b
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.
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