Find the least number b for divisibility What is the smallest positive integer $b$ so that 2014 divides $5991b + 289$?
I just need hints--I am thinking modular arithmetic?
This question was supposed to be solvable in 10 minutes...

${\rm mod}\ 2014\!:\ b\equiv \dfrac{-289}{5991}\overset{\large\frown}\equiv\dfrac{0}{2014}\overset{\large\frown}\equiv\dfrac{-289}{-51}\overset{\large\frown}\equiv\dfrac{813}{25}\overset{\large\frown}\equiv\dfrac{-677}{-1}\ $ by fractional ext. Euclidean.
