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