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Mathematics Colloquium: A Universal Method for Proving Recurrence Sequence Indentities
4:10 p.m. Neill 5W
In the past 300 years, mathematicians have discovered hundreds if not thousands of identities involving the Fibonacci and Lucas numbers and more generalized recurrence sequences. Some identities can be proved by simple induction, but many have required very long and complex methods of proof. Also, a method which works on one identity may not be useful on another identity. We will present a universal method which can be used to prove essentially any identity involving recurrence sequences, by reducing the proof to a simple numerical calculation. This will result in an algorithm which can be implemented on a computer.