## Fibonacci Num3ers | x^2 + y^2 + x = 3*x*y

Prove that if a pair of positive integers   $(x, \; y)$   satisfies the equation

$x^2 \; + \; y^2 \; + \; x \; = \; 3 \, x \, y$

then

$x \; = \; ( \,F_{2n+1} \,)^2$
$y \; = \; ( \,F_{2n} \,)^2 \; + \; 1$        or        $y \; = \; ( \,F_{2 \,n+2} \,)^2 \; + \; 1$

Advertisements

## About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.