1991 AIME Problem 13

A drawer contains a mixture of red socks and blue socks, at most 1991 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly \frac{1}{2} that both are red or both are blue. What is the largest possible number of red socks in the drawer that is consistent with this data?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.