A Texas oilman who was an amateur number theorist opened a new bank account by depositing a certain integral number of dollars, which we shall call x.
His second deposit, y, also was an integral number of dollars.
Thereafter each deposit was the sum of the two previous deposits.
(In other words, his deposits formed a generalized Fibonacci series.)
His 20th deposit was exactly a million dollars.

What are the values of x and y, his first two deposits?

Source: problem by Leonard A. Monzert

(In reply to Solution by Brian Smith)

Very cool solutions, Brian and Charlie!  I particularly like that Brian proved the solution was unique.

Posted by Steve Herman on 2016-01-05 13:37:50