Exploring the World of p-adic Numbers
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Questions and Answers

Which concept is used in the p-adic number system to determine closeness between numbers?

  • Power
  • Divisibility (correct)
  • Congruence
  • Absolute value

    • Who first described the p-adic numbers?

  • Ernst Kummer
  • Fermat
  • Andrew Wiles
  • Kurt Hensel (correct)

    • What is the main motivation behind the development of p-adic numbers?

  • To extend the arithmetic of rational numbers
  • To prove Fermat's Last Theorem
  • To encode congruence information
  • To bring the ideas and techniques of power (correct)

    • What is the key property of p-adic numbers that enables them to encode congruence information?

    <p>Divisibility</p> Signup and view all the answers

    What is the famous theorem that p-adic numbers have powerful applications in?

    <p>Fermat's Last Theorem</p> Signup and view all the answers

    Which set of numbers is a subset of the set of integers?

    <p>Natural numbers</p> Signup and view all the answers

    Which numbers can be considered as integers?

    <p>All of the above</p> Signup and view all the answers

    Which numbers are not considered as integers?

    <p>All of the above</p> Signup and view all the answers

    What is the smallest group and ring containing the natural numbers?

    <p>Integers</p> Signup and view all the answers

    How are negative numbers related to positive numbers in the set of integers?

    <p>Negative numbers are the additive inverses of positive numbers</p> Signup and view all the answers

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