Deposits

#	Amount ($)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

A Silicon Valley programmer/math hobbyist is selling shares of stock and depositing the money in a savings account. The first deposit is x, and the second deposit is y, where both dollar amounts are whole numbers (no cents). Each subsequent deposit is the sum of the two previous deposits. The 20th deposit is exactly one million dollars. Find x and y.

Hint: This pattern forms a generalized Fibonacci series.

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Analysis

The diophantine equation is: F18 x + F19 y = 1,000,000, where F18 = 2584 and F19 = 4181.