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All the term of the sequence are perfect squares

Source: Bulgarian MO 2003: P3

May 22, 2014
inductionalgebra unsolvedalgebra

Problem Statement

Given the sequence {yn}n=1∞\{y_n\}_{n=1}^{\infty} defined by y1=y2=1y_1=y_2=1 and yn+2=(4k−5)yn+1−yn+4−2k,n≥1y_{n+2} = (4k-5)y_{n+1}-y_n+4-2k, \qquad n\ge1 find all integers kk such that every term of the sequence is a perfect square.
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