Given the sequence $\{y_n\}_{n=1}^{\infty}$ defined by $y_1=y_2=1$ and \[y_{n+2} = (4k-5)y_{n+1}-y_n+4-2k, \qquad n\ge1\] find all integers $k$ such that every term of the sequence is a perfect square.
Source: Bulgarian MO 2003: P3
Tags: induction, algebra unsolved, algebra
Given the sequence $\{y_n\}_{n=1}^{\infty}$ defined by $y_1=y_2=1$ and \[y_{n+2} = (4k-5)y_{n+1}-y_n+4-2k, \qquad n\ge1\] find all integers $k$ such that every term of the sequence is a perfect square.