If a, b, and c are three consecutive terms of the Fibonacci sequence,
Determine the value(s) of ac - b2.
Solution to the Problem:
The answer is 1 and -1.Make a chart to examine the first several triples and look for a pattern.
| a | b | c | ac - b2 |
|---|---|---|---|
| 1 | 1 | 2 | 2 - 1 = 1 |
| 1 | 2 | 3 | 3 - 4 = -1 |
| 2 | 3 | 5 | 10 - 9 = 1 |
| 3 | 5 | 8 | 24 - 25 = -1 |
| 5 | 8 | 13 | 65 - 64 = 1 |
Hari Kishan sent in a much more rigorous analysis of the problem:
Correctly solved by:
| 1. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 2. Veena Mg | Bangalore, Karnataka, India |
| 3. Hari Kishan | Meerut, Uttar Pradesh, India |
| 4. K M Thomas | Pune, Maharashtra, India |
| 5. Kelly Stubblefield | Mobile, Alabama |