- #1

Imaginer1

- 6

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So, formally:

1) There exists no entry in the Fibbonacci sequence F(n) such that neither F(n) or F(n+1) are the sum of two squares

2) There an infinite number of n that F(n), F(n-1) and F(n+1) are all the sum of two squares.

Less formally:

Why do numbers that are the sum of two squares 'like' to group together in twos and threes?

Why do numbers that are not the sum of two squares like to be apart from each other?