• This was also published in 1225 and is known as Fibonacci's most remarkable work. This book revolves around number theory where Fibonacci examines methods used to find Pythagorean triples and how to construct square numbers using sums of odd numbers as well. Within this book, Fibonacci goes on and proves results in number theory like proving there is no \(x\) such that \(x^2+y^2\) and \(x^2-y^2\) are both squares and how \(x^4-y^4\) can never be a square.  In addition, Fibonacci also defined a new concept, congruum, which is a number that is of the form \(ab(a+b)(a-b)\) and he notes that if \(a+b\) ends up even, then four times this if \(a+b\) is odd. He proves this and a few other applications within this concept.