Exercise · ZW-PELL-S-EQUATION-003 · ★☆☆ Basic
What is the solution with the smallest positive \(y\) of Pell's equation called?
Choose one option.
Show answer
- C. Fundamental solution
Explanation
The one with the smallest positive \(y\) is called the fundamental solution, and all others are generated from it. The other names describe different concepts.
Review the concept: Pell's equation
Pell's equation is the quadratic Diophantine equation in integers \(x\), \(y\) that sets equal to 1 the difference between \(x^2\) and \(d\) times \(y^2\), where \(d\) is a positive integer that is not a perfect square.
\[x^2 - d y^2 = 1\]
More practice problems: pell's equation
- ZW-PELL-S-EQUATION-001 Identify which of these equations is a Pell equation.
- ZW-PELL-S-EQUATION-002 State which of these values of d is valid for Pell's equation.
- ZW-PELL-S-EQUATION-004 Identify which property of √d allows solving Pell's equation with continued fractions.
- ZW-PELL-S-EQUATION-005 Which pair (x,y) is a solution of x^2 - 2y^2 = 1?
- ZW-PELL-S-EQUATION-006 Find the fundamental solution of x^2 - 3y^2 = 1 with minimal positive y.
- ZW-PELL-S-EQUATION-007 Compute the convergent p/q of the continued fraction of √2 that gives the solution of x^2-2y^2=1.
- ZW-PELL-S-EQUATION-008 Determine the fundamental solution of x^2 - 7y^2 = 1 knowing that 8^2 - 7· 3^2 = 1.
- ZW-PELL-S-EQUATION-009 If (2,1) is the fundamental solution of x^2-3y^2=1, which pair is obtained by computing (2+√3)^2?