111A09201B/9 has a remainder of 5. find the least value of A+B This is from a competitive mathematics contest and I have no idea how to go about solving it.
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$$1+1+1+A+0+9+2+0+1+B\equiv5(mod9),$$ which gives $$A+B\equiv8(mod9)$$ and we see that $8$ is the answer.