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...

Using the Extended Euclidean Algorithm as implemented in the Euclid-Wallis Algorithm:
$$
\begin{array}{r}
&&2&1&38&2&25\\\hline
1&0&1&-1&39&-79&2014\\
0&1&-2&3&-116&235&-5991\\
5991&2014&1963&51&25&1&0\\
\end{array}
$$
Therefore, $2014\cdot235-5991\cdot79=1\implies5991\cdot79+1\equiv0\pmod{2014}$.
Multiply the last equivalence by $289$ to get the equivalence
$$
5991\cdot b+289\equiv0\pmod{2014}
$$
for $b\equiv289\cdot79\pmod{2014}$.
