 They involve the general theme of adding or subtracting fractions of a pile or specific numbers of discrete objects and asking how many there could have been in the beginning.The next reference to a similar problem is in Jacques Ozanam's "Récréations mathématiques et physiques", 1725.In the realm of pure mathematics, Lagrange in 1770 expounded his continued fraction theorem and applied it to solution of Diophantine equations.