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.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.5: Convex Polygons

Problem 41E

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