jmc

The first $N$ positive odd integers are 1, 3, $\dots$, $2N-1$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the first $N$ positive odd integers is $$\frac{1+(2N-1)}{2}\cdot N=N^2.$$If $N^2=121$, then $N=\boxed{11}$.