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On The Positive Integer Solution to Diophantine Equation x~2-y~2=z~n

Wenzhong Zhang

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Abstract

This article provides a formula to positive integer soluations of Diophantine equation x2-y2=zn,it is more succinct than known formula,at the same time it provides a megnitude formula to solutions of all positive integer of this equation when z=m fixed.

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What this paper is about

This article provides a formula to positive integer soluations of Diophantine equation x2-y2=zn,it is more succinct than known formula,at the same time it provides a megnitude formula to solutions of all positive integer of this equation when z=m fixed.

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Available abstract

This article provides a formula to positive integer soluations of Diophantine equation x2-y2=zn,it is more succinct than known formula,at the same time it provides a megnitude formula to solutions of all positive integer of this equation when z=m fixed.

Key concepts: Diophantine equation, Integer (computer science), Diophantine set, Legendre's equation, Mathematics, Radical of an integer, Thue equation, Discrete mathematics

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