October 21, 2004 was Martin Gardner's 90

In tribute to Martin Gardner, this month's problem is paraphrased from his book "Wheels, Life, and Other Mathematical Amusements".

A rich woman deposits a whole number of dollars *x* in her bank.
The next time she deposits *y* dollars (still a whole number). Each
subsequent deposit is the sum of the two previous deposits. Her
20^{th} deposit is exactly one million dollars. Find
*x* and *y*.