Question about Linear Congruences

I'm reading a chapter on linear congruences such as

What is confusing me is this sentence, "we may ask how many of the m congruence classes modulo m give solutions; this is exactly the same as asking how many incongruent solutions there are modulo m".

Why are the congruence classes that give solutions considered incongruent? It would seem to me that is the opposite: they should be congruent solutions.

The example: Find all solutions to . A complete set of three incongruent solutions is given by x=8, x=13, x=3. I understand how to calculate those three values of x, I don't understand why they are calling these "incongruent solutions".

Re: Question about Linear Congruences

Quote:

Originally Posted by

**VinceW** I'm reading a chapter on linear congruences such as

What is confusing me is this sentence, "we may ask how many of the m congruence classes modulo m give solutions; this is exactly the same as asking how many incongruent solutions there are modulo m".

Why are the congruence classes that give solutions considered incongruent? It would seem to me that is the opposite: they should be congruent solutions.

The example: Find all solutions to

. A complete set of three incongruent solutions is given by x=8, x=13, x=3. I understand how to calculate those three values of x, I don't understand why they are calling these "incongruent solutions".

these are called mutually incongruent solutions because

now find any other which satisfies the congruence, that will be **congruent** (mod15) to either 3 or 8 or 13.

Re: Question about Linear Congruences

Ahh... Now it makes perfect sense. I'm glad I asked. Thanks!