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Later, Cauchy proved the result conjectured by Farey. Though, Charles Haros proved similar result in 1802 which were not known to Farey and Cauchy. Later, Farey sequence appeared in many different areas of mathematics, including number theory, topology, geometry, see, 151,13), [1]. Farey sequence is also related to Fords circle and Riemann hypothesis, 16).
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