منابع مشابه
The 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 کاملA Note on the Negative Pell Equation
We provide a new elementary proof of a criterion, given in earlier work, for the solvability of the Pell equation x2 −Dy2 = −1 where D is any positive nonsquare integer. Mathematics Subject Classification: Primary 11D09; 11A55; Secondary 11R11; 11R29
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 . . . . . . . . . . ....
متن کاملThe Pell Equation in Quadratic Fields
where 7 is a given integer of a quadratic field F, and integral solutions £, 77 are sought in F. It has been shown that equation (1) has an infinite number of solutions if and only if 7 is not totally negative when F is a real field, and 7 is not the square of an integer of F when F is imaginary. We now obtain the following result : Let 7 be such that equation (1) has an infinite number of solu...
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ژورنال
عنوان ژورنال: International Journal for Research in Applied Science and Engineering Technology
سال: 2019
ISSN: 2321-9653
DOI: 10.22214/ijraset.2019.2088