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

Source Work

 * The Dictionary
 * $11$
 * $11$

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.

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.