1. A primitive Pythagorean triple is an ordered tripe of integers (x, y, z) such that x² + y? = z?, where x, y and z are pairwisely relatively prime integers. Determine exactly 10 primitive Pythagorean triples and be able to exhibit that they satisfy the given equation. 2. Solve the system of congruence 3x + 7y = 10 ( mod 16) 5x + 2y = 9( mod 16) . Hint: Eliminate x by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only y as a variable. Likewise, eliminate y by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only x as a variable.
1. A primitive Pythagorean triple is an ordered tripe of integers (x, y, z) such that x² + y? = z?, where x, y and z are pairwisely relatively prime integers. Determine exactly 10 primitive Pythagorean triples and be able to exhibit that they satisfy the given equation. 2. Solve the system of congruence 3x + 7y = 10 ( mod 16) 5x + 2y = 9( mod 16) . Hint: Eliminate x by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only y as a variable. Likewise, eliminate y by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only x as a variable.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 33EQ
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