Relation between Square of Fibonacci Number and Square of Lucas Number/Mistake

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$11$


Mistake

Squaring the Fibonacci numbers, then alternately subtracting and adding $4$, produces the squares of the Lucas numbers:
$5 \times 1^2 - 4 = 1^2 \qquad 5 \times 1^2 + 4 = 3^2$
$5 \times 2^2 - 4 = 2^2 \qquad 5 \times 3^2 + 4 = 7^2 \qquad$ and so on.


Correction

The expression:

$5 \times 2^2 - 4 = 2^2$

should read:

$5 \times 2^2 - 4 = 4^2$

and it is noted that $4$ is indeed the third Lucas number.


Interestingly and oddly, this is correct in the first edition of Curious and Interesting Numbers of $1986$.


Sources