Thread: Congruence, prime number, integer

let p be odd prime, and a,b be integers
1) prove that the congruence always have one solution
2) when does the above congruence have 2 solutions modulo p?
3) solve the congruence

Originally Posted by Shurelia

let p be odd prime, and a,b be integers
1) prove that the congruence always have one solution
2) when does the above congruence have 2 solutions modulo p?
3) solve the congruence

The wording for part one is strange to me.

Consider



Since the integers mod p are a finite field they are an integral domain we have that



I cannot see any reason why [tex]a \equiv -b \mod{p}[\tex] So it looks like it can have two solutions.

Please clarify and see if this gets you started on the next problem.

For the last one just factor!