Question

We say that a solution n of a congruence is unique modulo c if any solution n' of it is congruent to n modulo c. Can you give me an example?

Answer 1

\(3x\equiv1(\text{mod }11)\) in \(\mathbb{Z}_{11}\)

Answer 2

only solution is \(4\), but if we change to \(\mathbb{Z}\) there are infinite solutions.

Answer 3

all solutions are x = 4 + 11k, right?

Answer 4

in \(\mathbb{Z}\)?

Answer 5

\(3(4+11k)-1=12+33k-1=11+33k=11(3k+1)\)

yep