Number Theory, Part 2

If two integers differ from each other by a multiple of some integer m, we say they are ______ modulo m

The set of all integers x such that x = b (mod m), denoted by [b], is referred to as a ________ class?

The above is an example of a _________ class.

What is the term for a set of integers, S, such that every integer that exists is congruent modulo m to some integer in S.

What is the term for a set of integers, S, such that every integer that exists that is relatively prime to m is congruent to some integer in S?

Let b and c be integers. If bc is congruent to 1 modulo m, what is the term for this multiplicative relationship that b has to c?

Integer b has an inverse modulo m precisely when b and m are ____ ____. (2 word answer)

What is the name of the following type of problem: Find x such that a*x is congruent to b modulo m? (where a, b, and m are known integers, and x is the unknown you are trying to solve for)

The linear congruence ax = b (mod m) has a solution when gcd(?, ?) divides b. Enter your answers separated by a comma.

The solutions to linear congruence ax = b (mod m) are separated by multiples of what number, where d = gcd(a, m). Write your answer as a fraction like this: x/y

Name the theorem: A system of n linear congruences in one variable x has a solution, if and only if all of the moduli are pairwise relatively prime

Name the theorem: An integer p is prime if and only if (p-1)! is congruent to (p - 1) modulo p. (Example: (5-1)! = 24 is congruent to (5 -1) = 4 modulo 5).