In Underwood Dudley's Number theory book second edition chapter 5 problem 7 I encountered this problem:
Solve $9x\equiv 4 \mod1453$
I know that since $gcd(9,1453)=1$, there exists a unique solution. I found the answer in the back to be 1292 but I have no clue how to find this without doing guess and check--a method I'm sure is not very efficient here.
Does anyone know how to go about solving this? If it helps, 1453 is prime.