Pell's Equation

Pell’s Equation

an equation of the form x² - Dy² = 1, where D is a positive integer that is not a perfect square and the equation is to be solved in integers. The equation has an infinite number of solutions. The solution x₀ = 1, y₀ = 0 is obvious. The next—in terms of magnitude—solution (x₁, y₁) of Pell’s equation can be found by expanding into a continued fraction. If we know the solution (x₁, y₁), the entire set of solutions (x_n y_n) can be obtained by using the formula

Pell’s equation is closely related to the theory of algebraic numbers. It is named after the 17th-century British mathematician J. Pell, to whom L. Euler incorrectly attributed a method of solving this equation.

REFERENCES

Venkov, B. A. Elementarnaia teoriia chisel. Moscow-Leningrad, 1937. Chapter 2.
Dickson, L. E. History of the Theory of Numbers, vol. 2. New York, 1966.

单词	pell's equation
释义	Pell's Equation Pell’s Equation an equation of the form x² - Dy² = 1, where D is a positive integer that is not a perfect square and the equation is to be solved in integers. The equation has an infinite number of solutions. The solution x₀ = 1, y₀ = 0 is obvious. The next—in terms of magnitude—solution (x₁, y₁) of Pell’s equation can be found by expanding into a continued fraction. If we know the solution (x₁, y₁), the entire set of solutions (x_n y_n) can be obtained by using the formula Pell’s equation is closely related to the theory of algebraic numbers. It is named after the 17th-century British mathematician J. Pell, to whom L. Euler incorrectly attributed a method of solving this equation. REFERENCES Venkov, B. A. Elementarnaia teoriia chisel. Moscow-Leningrad, 1937. Chapter 2. Dickson, L. E. History of the Theory of Numbers, vol. 2. New York, 1966.
随便看	position sensitive silicon detector position sensitive x-ray detector position sensor position sheet position sheets positions in counseling centers position size position sizes position sizing position specific isotope analysis position specific iterated basic local alignment search tool position specific posterior lattice position specific scoring matrix position statement position switched network position switched to service assistant position switched to service assistant trunk position switching position switching module position telemetering position trader position trader (futures) position traders position trading position transducer