Problem #81

October 21, 2004 was Martin Gardner's 90^th birthday. Gardner was the author of the "Mathematical Games" column in Scientific American from 1956 to 1986. Through his columns and books he popularized both recreational and "serious" mathematics and inspired a generations of young people to pursue mathematical careers. A partial list of his mathematical books is here.

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.