Antiquity. Works of Diofanta

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From 189 equations which have remained in ' to Arithmetics ', with all clearness it is visible that Diofant paid the main attention to the decision of the positive, rational uncertain equations, that is basically the equations having a great number of roots. Diofant was interested, however, only in one decisions - ' positive ' and ' rational '. In search of such decisions it has shown the big ingenuity in selection of factors.

From other works of Diofanta, except ' Arithmetics ', treatise fragments about repeated numbers and a fragment of reasonings on the Egyptian mathematics have remained.

Up to VI century except Diofanta there was no outstanding Greek mathematician. Works of Diofanta have brought the greatest advantage much later when in a science sky there were stars of the first magnitude: P.Ferma, L.Euler, K.Gauss. Works of Diofanta became subsequently a starting point of researches in the field of the theory of numbers of these well-known scientists. One of sections of the theory and is called ' diofantovy approach ' which, generally speaking, concern decisions of linear and nonlinear inequalities in integers. It is a lot of attention in the works such mathematicians, as A.Gurvits, K.Rot, G.Minkovsky, A.J.Hinchin and V.Serpinsky have devoted diofantovym priblizhenijam.

The mathematics included also the term ' diofantovy the equations '. This name concerns a problem of the decision of the equations with a great number unknown, than the equations or their system, besides in whole or rational numbers. For example, the equation ah + bу=with where and, b, with - integers, can be solved in integers only in case with has the greatest general divider with numbers and and b.

It is necessary to underline that at research of the theory of the specified equations begun by Diofantom in Alexandria, the major results are received by P.Ferma, L.Euler, Z.Lagranzhem, E.Kummerom, X. Tue, T.Skolemom and T.Nagellom. Modern researches in the field of the theory diofantovyh the equations are closely connected with the algebraic theory of numbers and the theory diofantovyh priblizheny.