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...re de|P. de Fermat]] wrote in the margin of his copy of the Arithmetika of Diophantus that: "Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-

...of indefinite equations. This point of view is systematically followed by Diophantus in his book. Even though his work contains solutions of specific Diophantin Diophantus in his Aritmetika deals with the search for rational (not necessarily integ

...(a special case of the [[Pell equation|Pell equation]]). In his Aritmetika Diophantus (3rd century B.C.) made an attempt to setting up a theory of indeterminate ...number is the sum of four squares of integers. It should be mentioned that Diophantus in his Aritmetika repeatedly used the possibility of representing a natural

...btraction operations. These are implicitly operations on negative numbers. Diophantus applied his own rules to rational numbers only (cf. [[Rational number|Ratio ...ry are based on Greek mathematics, in particular on the work of Euclid and Diophantus, this is not true of computational techniques. The development of arithmeti

...0 in the margins of his copy of the book Aritmetika [[#References|[1]]] by Diophantus as follows: "It is impossible to partition a cube into two cubes, or a biqu <TR><TD valign="top">[1]</TD> <TD valign="top"> Diophantus of Alexandria, "Aritmetika and the book on polygonal numbers" , Moscow (197

...istic era, thanks to the liberation of algebra from its geometric setting. Diophantus (probably 3th century A.D.) denoted the unknown $x$ and its powers by the f ...iota$ (from the Greek $\iota\sigma\omicron\varsigma$, equal). For example, Diophantus would have written the equation

...blems in number theory, and methods for their solution, was carried out by Diophantus (3rd century) in his Aritmetika, where, in particular, he gave solutions in

is "cubo-quadratic" , etc. (as long ago as Diophantus in the 3rd century, and later by a number of medieval authors). The idea of

...tion of quadratic equations was first expounded in the book Arithmetica by Diophantus (3rd century A.D.). In the 16th century, Italian mathematicians obtained th

...0.png" />) this problem had been considered even in Antiquity (Archimedes, Diophantus, Euclid), while its close connection with the theory of continued fractions

...tions were known even in early antiquity. In particular, the Arithmetic of Diophantus (3rd century A.D.) had a major influence on the development of algebraic id

...rmulate an algorithm for the solution of quadratic equations in all cases. Diophantus (3rd century) operated freely with negative numbers. They appear constantly