Modular arithmetic

  • Rational Round
    problem

    Rational Round

    Age
    16 to 18
    Challenge level
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    Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

  • Pythagoras mod 5
    problem

    Pythagoras Mod 5

    Age
    16 to 18
    Challenge level
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    Prove that for every right angled triangle which has sides with integer lengths: (1) the area of the triangle is even and (2) the length of one of the sides is divisible by 5.

  • Modular Fractions
    problem

    Modular Fractions

    Age
    16 to 18
    Challenge level
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    We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

  • Small Groups
    article

    Small Groups

    Learn about the rules for a group and the different groups of 4 elements by doing some simple puzzles.
  • Latin Squares
    article

    Latin Squares

    A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
  • The Knapsack Problem and Public Key Cryptography
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    The Knapsack Problem and Public Key Cryptography

    An example of a simple Public Key code, called the Knapsack Code is described in this article, alongside some information on its origins. A knowledge of modular arithmetic is useful.
  • The Chinese Remainder Theorem
    article

    The Chinese Remainder Theorem

    In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."

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