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Question 14: Number Theory - Fermat's Last Theorem for Specific Exponents Instructions: Use data from the link provided below and make sure to give your original work. Plagiarism will not be accepted. You can also use different colors and notations to make your work clearer and more visually appealing. Problem Statement: Prove that there are no non-zero integer solutions to the equation x² + y² = 24. Theoretical Parts: 1. Fermat's Last Theorem Overview: Provide an overview of Fermat's Last Theorem and its significance in number theory. 2. Case for Exponent 4: Explain why proving the theorem for the exponent 4 is a crucial step in the general proof. 3. Proof for Exponent 4: Using mathematical induction or other relevant methods, prove that the equation x + y² = 24 has no non-zero integer solutions. Data Link: https://drive.google.com/drive/folders/1C4dE5fGhljKIMnOpQrStUvWxYz89012

Question 14: Number Theory - Fermat's Last Theorem for Specific Exponents Instructions: Use data from the link provided below and make sure to give your original work. Plagiarism will not be accepted. You can also use different colors and notations to make your work clearer and more visually appealing. Problem Statement: Prove that there are no non-zero integer solutions to the equation x² + y² = 24. Theoretical Parts: 1. Fermat's Last Theorem Overview: Provide an overview of Fermat's Last Theorem and its significance in number theory. 2. Case for Exponent 4: Explain why proving the theorem for the exponent 4 is a crucial step in the general proof. 3. Proof for Exponent 4: Using mathematical induction or other relevant methods, prove that the equation x + y² = 24 has no non-zero integer solutions. Data Link: https://drive.google.com/drive/folders/1C4dE5fGhljKIMnOpQrStUvWxYz89012

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 28RE
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Question 14: Number Theory - Fermat's Last Theorem for Specific Exponents Instructions: Use data from the link provided below and make sure to give your original work. Plagiarism will not be accepted. You can also use different colors and notations to make your work clearer and more visually appealing. Problem Statement: Prove that there are no non-zero integer solutions to the equation x² + y² = 24. Theoretical Parts: 1. Fermat's Last Theorem Overview: Provide an overview of Fermat's Last Theorem and its significance in number theory. 2. Case for Exponent 4: Explain why proving the theorem for the exponent 4 is a crucial step in the general proof. 3. Proof for Exponent 4: Using mathematical induction or other relevant methods, prove that the equation x + y² = 24 has no non-zero integer solutions. Data Link: https://drive.google.com/drive/folders/1C4dE5fGhljKIMnOpQrStUvWxYz89012
Transcribed Image Text:Question 14: Number Theory - Fermat's Last Theorem for Specific Exponents Instructions: Use data from the link provided below and make sure to give your original work. Plagiarism will not be accepted. You can also use different colors and notations to make your work clearer and more visually appealing. Problem Statement: Prove that there are no non-zero integer solutions to the equation x² + y² = 24. Theoretical Parts: 1. Fermat's Last Theorem Overview: Provide an overview of Fermat's Last Theorem and its significance in number theory. 2. Case for Exponent 4: Explain why proving the theorem for the exponent 4 is a crucial step in the general proof. 3. Proof for Exponent 4: Using mathematical induction or other relevant methods, prove that the equation x + y² = 24 has no non-zero integer solutions. Data Link: https://drive.google.com/drive/folders/1C4dE5fGhljKIMnOpQrStUvWxYz89012
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