Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that the equation x4-y4 = z² has no integer solutions.

Prove that the equation x4-y4 = z² has no integer solutions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Solve (b) part only in 30 min plz plz and don't want answer from any other site if u post some one else answer i will give you thumb down Be sure to give me 100 ? percent exact answer and take a thumb up thanks your answer will be appreciated
1. (a) Suppose we have a right-angled triangle and a square of equal area, both of which have side of integer length. Show that this implies the existence of integers p and q with p q and for which p4- q¹ is a square. (Hint: you may find Theorem 1.2 in the notes useful here.) (b) Prove that the equation x4-y4 = z² has no integer solutions. (c) Show that the area of a triangle whose sides have integer length is never the square of an integer.
Transcribed Image Text:1. (a) Suppose we have a right-angled triangle and a square of equal area, both of which have side of integer length. Show that this implies the existence of integers p and q with p q and for which p4- q¹ is a square. (Hint: you may find Theorem 1.2 in the notes useful here.) (b) Prove that the equation x4-y4 = z² has no integer solutions. (c) Show that the area of a triangle whose sides have integer length is never the square of an integer.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS