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

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- Jun 8th 2011, 06:28 AMShureliaCongruence, 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 - Jun 8th 2011, 09:10 AMTheEmptySet
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!