If you assume you could prove (5) and (6) by induction where your base cases are when , which are (3) and (4) respectively.
I read some facts about Lucas sequences, but they were not proven, can you help me?
Let P and Q be integers. Define with .
Similar define with .
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(1) (Managed to prove by induction myself)
(2)
(3)
(4)
(5)
(6)
I would be thankful for any proven statement .