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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $11$