The work presents the Farey sequence, its motivation and properties. A recursive formula for calculating the length of the sequence of order n and its asymptotic behaviour are stated. The Farey sequence is in bijection with the set of Ford circles, therefore a geometric meaning of the mediant and the neighbours property is explained as well as the construction of all Ford neighbours to a given Ford circle. Moreover, Ford spheres are defined. Using the fact that the group of Möbius transformations acts on the set of Ford circles, the mediant property for Ford circles is proved. Additionally, the Riemann hypothesis and two of its equivalent statements are presented. A theorem, connecting the Farey sequence, the Mertens function and the Riemann hypothesis, is proved.
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