Question 16
All the positive integers which are co-prime to $2012$ are grouped in an increasing order in such a way that the $n$th group has $2n-1$ numbers. So, the first three groups in this grouping are $(1)$, $(3,5,7)$, $(9,11,13,15,17)$. It is known that $2013$ belongs to the $k$th group. Find the value of $k$.
(Note: Two integers are said to be co-prime if their greatest common divisor is $1$.)
(Note: Two integers are said to be co-prime if their greatest common divisor is $1$.)