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How did Aryabhata solve linear indeterminate equations with the kuttakara method?
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Indian mathematics
The evolution of Hindu-Arabic numerals from Brahmi through Devanagari and Arabic to European scripts.
In the context of Indian mathematics, the kuttakara (or "pulverizer") method was Aryabhataās general approach for solving linear indeterminate equations.
Rather than using a single formula, the method consisted of breaking down a complex problem into a series of new problems with successively smaller coefficients. This iterative process is essentially equivalent to the Euclidean algorithm and is closely related to the modern mathematical concept of continued fractions. By systematically reducing the size of the numbers involved, Aryabhata was able to find integer solutions for equations that would otherwise be difficult to resolve.1