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Sequence with each term perfect square

Source: Bosnia and Herzegovina TST 2013 problem 2

May 20, 2013
algebrapolynomialinductionalgebra proposed

Problem Statement

The sequence ana_n is defined by a0=a1=1a_0=a_1=1 and an+1=14an−an−1−4a_{n+1}=14a_n-a_{n-1}-4,for all positive integers nn. Prove that all terms of this sequence are perfect squares.
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