Fibonacci squares are rare!

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Is there a fibonacci type sequence that contains infinitely many squares? And one that doesn't contain any? And what about the cubes and other powers? There's so much questions I have right now... Your shorts are great, Michael, you manage to make them entertaining and you choose very interesting topics. Can't wait for the video about this one!

apollo
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Are there any numbers that besides 2&3 both fibonacci and Lucas numbers ?

skalderman
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No, not every mathematician likes these useless ideas

mcqueen