A positive integer N is said to be a congruent number if it is the area of a right triangle with rational side lengths. For example, 6 is a congruent number because it is the area of the 3 - 4 - 5 triangle and 5 is a congruent number because it is the area of the 3/2 – 20/3 - 41/6 triangle. (a) Let and A = {(X,Y,Z) € Q¹ = }XY = N₁X² + y² = z²¹} E : B = {(x, y) = Q² : y² = x³ - N²x, y ‡ 0} . Show that f(X,Y,Z) = (₁ 242) and g(x, y) = (№2²-2², -23N, N²+2²) -NY 2N² Y Y provide a bijection between the sets A and B.
A positive integer N is said to be a congruent number if it is the area of a right triangle with rational side lengths. For example, 6 is a congruent number because it is the area of the 3 - 4 - 5 triangle and 5 is a congruent number because it is the area of the 3/2 – 20/3 - 41/6 triangle. (a) Let and A = {(X,Y,Z) € Q¹ = }XY = N₁X² + y² = z²¹} E : B = {(x, y) = Q² : y² = x³ - N²x, y ‡ 0} . Show that f(X,Y,Z) = (₁ 242) and g(x, y) = (№2²-2², -23N, N²+2²) -NY 2N² Y Y provide a bijection between the sets A and B.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 5 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage