Do You Know Pell's Equation?

10 Questions | By Zlatanaleksic | Updated: Mar 21, 2022 | Attempts: 150

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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
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
3.

In Cartesian coordinates, what form does the Pell's equation have?
- A.
  
  Ellipse
- B.
  
  Circle
- C.
  
  Hyperbola
- D.
  
  Parabola
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
5.

Where was the equation studied extensively for the first time?
- A.
  
  India
- B.
  
  Italy
- C.
  
  Germany
- D.
  
  England
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
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)
8.

Who made the first significant progress in solving the Pell’s equation?
- A.
  
  Mahavira
- B.
  
  Varahamihira
- C.
  
  Yativṛṣabha
- D.
  
  Brahmagupta
9.

What did Bhāskarāchārya developed for solving Pell's equation?
- A.
  
  Chakravala method
- B.
  
  Geometric method
- C.
  
  Graphic method
- D.
  
  Muller's method
10.

When was William Brouncker born?
- A.
  
  1596
- B.
  
  1605
- C.
  
  1620
- D.
  
  1643