Book Review: Solving the Pell equation
نویسندگان
چکیده
منابع مشابه
Solving the Pell Equation, Volume 49, Number 2
to be solved in positive integers x , y for a given nonzero integer d. For example, for d = 5 one can take x = 9, y = 4. We shall always assume that d is positive but not a square, since otherwise there are clearly no solutions. The English mathematician John Pell (1610– 1685) has nothing to do with the equation. Euler (1707–1783) mistakenly attributed to Pell a solution method that had in fact...
متن کاملThe Pell Equation
Leonhard Euler called (1) Pell’s Equation after the English mathematician John Pell (1611-1685). This terminology has persisted to the present day, despite the fact that it is well known to be mistaken: Pell’s only contribution to the subject was the publication of some partial results of Wallis and Brouncker. In fact the correct names are the usual ones: the problem of solving the equation was...
متن کاملSolving constrained Pell equations
Consider the system of Diophantine equations x2 − ay2 = b, P (x, y) = z2, where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s method to produce an upper bound on the integer solutions. We present a general elementary approach, based on an idea of Cohn and the theory of the Pell equation, that solves many such systems. We apply the approach to th...
متن کاملPell ’ s Equation
An arbitrary quadratic diophantine equation with two unknowns can be reduced to a Pell-type equation. How can such equations be solved? Recall that the general solution of a linear diophantine equation is a linear function of some parameters. This does not happen with general quadratic diophantine equations. However, as we will see later, in the case of such equations with two unknowns there st...
متن کاملPell ’ s equation
1 On the so–called Pell–Fermat equation 2 1.1 Examples of simple continued fractions . . . . . . . . . . . . . 2 1.2 Existence of integer solutions . . . . . . . . . . . . . . . . . . 5 1.3 All integer solutions . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 On the group of units of Z[ √ D] . . . . . . . . . . . . . . . . . 8 1.5 Connection with rational approximation . . . . . . . . . . ....
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2014
ISSN: 0273-0979,1088-9485
DOI: 10.1090/s0273-0979-2014-01483-1