## anonymous one year ago 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?

1. zzr0ck3r

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

2. zzr0ck3r

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

3. anonymous

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

4. zzr0ck3r

in $$\mathbb{Z}$$?

5. zzr0ck3r

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