The arithmetic mean of two numbers m and n is given by (m + n)/2.

The geometric mean of two numbers m and n is given by √(mn).

For two positive integers m and n with m ≥ n, their arithmetic mean and geometric mean are consecutive odd integers. (For example, 7 and 9 are consecutive odd integers.)

How many possible values of m and n are there if both are less than 500? What is the largest such pair?