Putnam 1993

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Problem A2

The sequence an of non-zero reals satisfies an2 - an-1an+1 = 1 for n ≥ 1. Prove that there exists a real number α such that an+1 = α an - an-1 for n ≥ 1.

 

Solution

Trivial.

For n ≥ 2 define bn = (an + an-2)/an-1. Then the relation given shows that bn+1 = bn.

 


 

Putnam 1993

© John Scholes
jscholes@kalva.demon.co.uk
12 Dec 1998