Mathematical induction

  • Farey Neighbours
    problem

    Farey neighbours

    Age
    16 to 18
    Challenge level
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    Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

  • Particularly general
    problem

    Particularly general

    Age
    16 to 18
    Challenge level
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    By proving these particular identities, prove the existence of general cases.