A contribution of diophantus to mathematics the following is a statement of arithmetica book ii, problem 28 and its solution. Diophantus of alexandria, arithmetica and diophantine equations. Book x presumably greek book vi deals with rightangled triangles with rational sides and subject to various further conditions. For simplicity, modern notation is used, but the method is due to diophantus. Intersection of the line cb and the circle gives a rational point x 0,y 0. Immediately preceding book i, diophantus gives the following definitions to solve these simple problems. If a problem leads to an equation in which certain terms are equal to terms of the same species. The eighth problem of the second book of diophantus s arithmetica is to divide a square into a sum of two squares. Diophantus s main achievement was the arithmetica, a collection of arithmetical problems involving the solution of determinate and indeterminate equations.
This paper discusses some crucial issues related to diophantus problem solving. For example, the first seven problems of the second book fit much better with the problems of the first, as do problems ii, 17, and ii, 18. One of the most famous problems that diophantus treated was writing a square as the sum of two squares book ii, problem 8 to divide a given. According to our terminology, it is definitely a book on arithmetic, not in the ring of. Problem find two square numbers such that the sum of the product of the two numbers with either number is also a square number. The problems in book i of the arithmetica are determinate ie, having a unique solution or a. Diophantine equations i putnam practice october 27, 2004 in his book arithmetica diophantus discussed the problem of. Diophantus of alexandria arithmetica book i joseph. On the other hand, there is nothing improbable in the supposition that.
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