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Table of Contents:

Chapter One: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Questions
1.4 Objectives of the Study
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter Two: Literature Review
2.1 Historical Background of Continued Fractions and Pellʼs Equation
2.2 Definitions and Properties of Continued Fractions
2.3 Solving Pellʼs Equation using Continued Fractions
2.4 Previous Studies on Continued Fractions and Pellʼs Equation

Chapter Three: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Procedure
3.5 Ethical Considerations

Chapter Four: Discussion of Findings
4.1 Analysis of Continued Fractions and Pellʼs Equation
4.2 Comparison of Different Solution Methods
4.3 Implications of Findings
4.4 Future Research Directions

Chapter Five: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusions Drawn from the Study
5.3 Recommendations for Further Research
5.4 Overall Reflection on the Study

Overview: Number Theory: Continued Fractions and Pellʼs Equation

The thesis on Number Theory: Continued Fractions and Pellʼs Equation explores the relationship between continued fractions and Pellʼs equation, a fundamental problem in number theory. The study aims to investigate the properties of continued fractions and their application in solving Pellʼs equation, which has important implications in various fields such as cryptography and mathematical modeling.

Chapter One provides an introduction to the topic, outlining the background, problem statement, research questions, objectives, significance, limitations, and scope of the study. Chapter Two reviews the existing literature on continued fractions and Pellʼs equation, including historical background, definitions, properties, and previous studies.

Chapter Three discusses the research methodology, including the research design, data collection methods, analysis techniques, sampling procedure, and ethical considerations. Chapter Four presents the findings of the study, analyzing the properties of continued fractions, different solution methods for Pellʼs equation, and implications of the findings for future research.

Chapter Five concludes the thesis by summarizing the findings, drawing conclusions, providing recommendations for further research, and reflecting on the overall study. Overall, the thesis aims to contribute to the understanding of continued fractions and Pellʼs equation, shedding light on their significance in the field of number theory.

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