Diophantine equations

Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT). However, many still find it challenging to solve this problem.

13p viarnault 25-04-2024 2 1   Download

Lecture Cryptography and network security: Chapter 2 after studying this section will help you understand: To review integer arithmetic, concentrating on divisibility and finding the greatest common divisor using the Euclidean algorithm; To understand how the extended Euclidean algorithm can be used to solve linear Diophantine equations, to solve linear congruent equations, and to find the multiplicative inverses;...

82p hoathachthao090 10-02-2022 19 4   Download

In this paper, we prove the solutions of the exponential Diophantine equation 2x − 3y = z2 where x, y and z are non-negative integers. To find the solution, Catalan ’s conjecture and division algorithm congruence were applied. The result indicates that the equation has three solutions (x, y, z) including (0, 0, 0), (1, 0, 1) and (2, 1, 1).

4p trinhthamhodang9 10-12-2020 11 2   Download

Lifting The Exponent Lemma is a powerful method for solving exponential Diophantine equations. It is pretty well-known in the Olympiad folklore though its origins are hard to trace. Mathematically, it is a close relative of the classical Hensel’s lemma in number theory (in both the statement and the idea of the proof). In this article we analyze this method and present some of its applications.

12p lilymimi0404 26-08-2015 50 5   Download

Annals of Mathematics This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...

51p noel_noel 17-01-2013 46 7   Download

Part I Formalisms for Computation: Register Machines, Exponential Diophantine Equations, & Pure LISP 19 21 In Part I of this monograph, we do the bulk of the preparatory work that enables us in Part II to exhibit an exponential diophantine equation that encodes the successive bits of the halting probability . In Chapter 2 we present a method for compiling register machine programs into exponential diophantine equations. In Chapter 3 we present a stripped-down version of pure LISP.

0p xuongrong_battien 24-10-2011 46 2   Download