1. A primitive Pythagorean triple is an ordered tripe of integers (x, y, z) such thatx² + y? = z?,where x, y and z are pairwisely relatively prime integers. Determine exactly 10 primitive Pythagoreantriples and be able to exhibit that they satisfy the given equation.2. Solve the system of congruence3x + 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 alinear congruence containing only y as a variable. Likewise, eliminate y by multiplying each congruencea suitable constant and then adding them to form a linear congruence containing only x as a variable.3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n + 6.Hint: Recall that in the formula for finding the n-th triangular number, the numerator is a product of twoconsecutive integers.4. A palindrome number is a number that remains the same when its digits are reversed. For example, thefollowing numbers are palindromes:7 22 1315665 10 901480 084.Show that a palindrome with an even number of digits is divisible by 11. Hint: Read your notes.

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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.

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.

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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Question

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.
3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n + 6.
Hint: Recall that in the formula for finding the n-th triangular number, the numerator is a product of two
consecutive integers.
4. A palindrome number is a number that remains the same when its digits are reversed. For example, the
following numbers are palindromes:
7 22 131
5665 10 901
480 084.
Show that a palindrome with an even number of digits is divisible by 11. Hint: Read your notes.

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