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Determine a_2007 in an 'exact' sequence

Source: Baltic Way 2007

November 30, 2010

inductionalgebra proposedalgebra

Problem Statement

A sequence of integers

a_1,a_2,a_3,\ldots

is called exact if

a_n^2-a_m^2=a_{n-m}a_{n+m}

for any

n>m

. Prove that there exists an exact sequence with

a_1=1,a_2=0

and determine

a_{2007}

.

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