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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PLS. ANSWER NUMBER 1 AND 2 ONLY.
Transcribed Image Text: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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
