# Pell's Equation and Degenerate Lucas Sequences

## Question

1. 5x² - y² = -4
The solution is (x,y) = (1,3), but how to get it ? Please write a detailed explanation.

2. Degenerate Lucas Sequences
Let (P, Q) be such that the ratio α/β of roots of x² - Px + Q be a root of unity. Then the sequences U(P, Q), V(P, Q) are said to be degenerate.
Using plain English, please describe all degenerate sequences.

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