I know how to make the list of the Fibonacci numbers, but i don\'t know how can i test if a given number belongs to the fibonacci list - one way that comes in mind is genera
How big are the numbers you're dealing with?
Could a lookup table work for you? (a precomputed list of numbers you can search in)
There's also a closed-form expression that I guess you could invert to get at the answer analytically (though I'm no mathematician, so I can't promise this suggestion makes sense)