3. Intermediate Equation - Deepstash

3. Intermediate Equation

proposed some methods to solve equations of the type ax + by = c. According to Majumdar, Brahmgupta used continued fractions to solve such equations. He also tried to solve quadratic equations of the type ax² + c = y² and ax² – c = y². For example, for the equation 8x² + 1 = y² he obtained the solutions as (x, y)= (1, 3), (6, 17), (35, 99), (204, 577), (1189, 3363),..He also solved 61x² + 1 = y² having solution as x = 226153980, y = 1766319049 as its smallest solution.

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vedarham

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