Do You Know Pell's Equation?

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| By Zlatan Aleksic
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Zlatan Aleksic
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Do You Know Pells Equation? - Quiz

Pell's equation is used in mathematics when there is an equation with two or more unknowns. If you want to challenge your knowledge and test your informations, take this quiz!


Questions and Answers
  • 1. 

    Who was the first European that found the solution for Pell's equation?

    • A.

      William Brouncker

    • B.

      John Pell

    • C.

      Bathsua Makin

    • D.

      Leonhard Euler

    Correct Answer
    A. William Brouncker
    Explanation
    William Brouncker is the correct answer because he was the first European mathematician to find the solution for Pell's equation. Pell's equation is a mathematical equation of the form x^2 - ny^2 = 1, where n is a positive nonsquare integer. Brouncker's solution to this equation was published in 1657, making him the first to find a general solution for it. John Pell, Bathsua Makin, and Leonhard Euler were not specifically known for their contributions to Pell's equation.

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  • 2. 

    Who has mistakenly attributed Lord Brouncker's solution of the equation to John Pell?

    • A.

      Johann Bernoulli

    • B.

      Leonhard Euler

    • C.

      John Pell

    • D.

      Pierre Bouguer

    Correct Answer
    B. Leonhard Euler
    Explanation
    Leonhard Euler mistakenly attributed Lord Brouncker's solution of the equation to John Pell.

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  • 3. 

    In Cartesian coordinates, what form does the Pell's equation have?

    • A.

      Ellipse

    • B.

      Circle

    • C.

      Hyperbola

    • D.

      Parabola

    Correct Answer
    C. Hyperbola
  • 4. 

    Who was the first European that concluded that if n is not a perfect square, Pell's equation can have infinite distinct integer solutions?

    • A.

      John Pell

    • B.

      Narayana Pandit

    • C.

      William Brouncker

    • D.

      Joseph Louis Lagrange

    Correct Answer
    D. Joseph Louis Lagrange
    Explanation
    Joseph Louis Lagrange was a renowned mathematician who made significant contributions to number theory, including the study of Pell's equation. Pell's equation is a Diophantine equation of the form x^2 - ny^2 = 1, where n is a non-square positive integer. Lagrange concluded that if n is not a perfect square, Pell's equation can have infinite distinct integer solutions. His work on Pell's equation laid the foundation for further research and understanding of the equation, making him the first European to reach this conclusion.

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  • 5. 

    Where was the equation studied extensively for the first time?

    • A.

      India

    • B.

      Italy

    • C.

      Germany

    • D.

      England

    Correct Answer
    A. India
    Explanation
    India is the correct answer because the question asks where the equation was studied extensively for the first time. India is known for its rich history in mathematics, with scholars like Aryabhata and Brahmagupta making significant contributions to the field. The concept of equations and their study would have been explored extensively in ancient India, making it the likely place where the equation was first studied in depth.

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  • 6. 

    With which subject in mathematics does Pell's equation have connections?

    • A.

      Chebyshev polynomials

    • B.

      Continued fractions

    • C.

      Algebraic number theory

    • D.

      All of the above

    Correct Answer
    D. All of the above
    Explanation
    Pell's equation is a mathematical equation that is connected to all three subjects mentioned: Chebyshev polynomials, continued fractions, and algebraic number theory. Chebyshev polynomials are used in solving Pell's equation, continued fractions can be used to approximate solutions to Pell's equation, and algebraic number theory provides a deeper understanding of the properties and solutions of Pell's equation. Therefore, the correct answer is "All of the above."

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  • 7. 

    What is the Brouncker's solution for the equation (see picture) that was made by Fermat in 1657 to chalenge his fellows mathematicians?

    • A.

      (x,y) = (32188120829134849,181938015856460)

    • B.

      (x,y) = (1,2)

    • C.

      (x,y) = (176619049,226153980)

    • D.

      (x,y) = (0,-1)

    Correct Answer
    A. (x,y) = (32188120829134849,181938015856460)
  • 8. 

    Who made the first significant progress in solving the Pell’s equation?

    • A.

      Mahavira

    • B.

      Varahamihira

    • C.

      Yativṛṣabha

    • D.

      Brahmagupta

    Correct Answer
    D. Brahmagupta
    Explanation
    Brahmagupta made the first significant progress in solving the Pell's equation.

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  • 9. 

    What did Bhāskarāchārya developed for solving Pell's equation?

    • A.

      Chakravala method

    • B.

      Geometric method

    • C.

      Graphic method

    • D.

      Muller's method

    Correct Answer
    A. Chakravala method
    Explanation
    Bhāskarāchārya developed the Chakravala method for solving Pell's equation. This method is a mathematical algorithm that involves manipulating and simplifying the equation using a series of steps. It is particularly useful for finding integer solutions to Pell's equation, which is a type of Diophantine equation. The Chakravala method has been widely recognized for its efficiency and effectiveness in solving this type of equation.

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  • 10. 

    When was William Brouncker born?

    • A.

      1596

    • B.

      1605

    • C.

      1620

    • D.

      1643

    Correct Answer
    C. 1620
    Explanation
    William Brouncker was born in 1620.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Mar 15, 2018
    Quiz Created by
    Zlatan Aleksic
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