I have a book by Posamentier titledThe Fabulous Fibonacci Numbers. He's a top-notch author who puts out excellent books. In this book he lists much detail about the Fibonacci numbers (and the Lucas numbers too).

He threw in everything but the kitchen sink. Therefore I was amazed that a certain detail was missed in his book that I want to relate on this particular subforum as Fibonacci numbers is a definite number theory subject and the article I read overnight relates those group of numbers to a Hilbert problem (his tenth one).

This tenth Hilbert problem (concerning the solvability of Diophantine equations) was itself only solved in 1970 with the help of the Fibonacci numbers. The article is enjoyable reading and not too technical which can be read from this website: Hilbert's Tenth Problem: a History of Mathematical Discovery

I hope you find the article interesting.