Suppose that the system of linear Diophantine equations has solutions of the form x + 5y + 2z = 158 9y-z = 247 x = xo + Ak, y=yo+Bk, z = zo + CK, for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions. KEZ
Suppose that the system of linear Diophantine equations has solutions of the form x + 5y + 2z = 158 9y-z = 247 x = xo + Ak, y=yo+Bk, z = zo + CK, for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions. KEZ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with this Intro to Elementary Number Theory homework problem.
covered topics
- prime numbers
- linear Diophantine equations
- systems of linear Diophantine equations.
![Suppose that the system of linear Diophantine equations
has solutions of the form
x + 5y + 2z = 158
9yz = 247
x = xo + Ak, y = yo + Bk, 2 = 20 + Ck, kez
for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F988321fe-2fa3-453d-a72b-be5ece348fb5%2F52afd2f8-bda8-44a2-b48d-a475ce5e9de6%2Fhvmwdc_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the system of linear Diophantine equations
has solutions of the form
x + 5y + 2z = 158
9yz = 247
x = xo + Ak, y = yo + Bk, 2 = 20 + Ck, kez
for some integer constants A, B, C. Find the smallest positive value of x among all of the solutions.
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