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sequence problem

Source: China South East Mathematical Olympiad 2011

August 18, 2011
inductionalgebra proposedalgebra

Problem Statement

The sequence (an)n>=1(a_n)_{n>=1} satisfies that : a1=a2=1a_1=a_2=1 an=7an−1−an−2a_n=7a_{n-1}-a_{n-2} (n>=3n>=3) , prove that : for all positive integer n , number an+2+an+1a_n+2+a_{n+1} is a perfect square .
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