A new relation to find all natural solutions to hyperbola and Diophantine equations using Pell's equation | ||
| Journal of College of Education for Pure Science | ||
| Article 1, Volume 6, Issue 1, December 2016, Pages 30-42 | ||
| Author | ||
| Evan Abdulkareem Huzam | ||
| Abstract | ||
| In this paper a new relation has been found between any natural solution to the hyperbola equationx^2-dy^2=c^2, where cϵN,d a positive square free numberand a form that gives allnatural solutions to Pell'sequationx^2-dy^2=1. Which enable us to obtain all natural solutions for the above hyperbola equation thena square natural numberu for the Diophantine equation u=(m^2+n^2)/(1+mn) where (m,n)∈N. | ||
| Keywords | ||
| Diophantine equation; Pell; continued fraction | ||
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