Find all solutions to the following Diophantine equations. i. 35x + 25y = 8 ii. 35x + 25y = 15 iii. 47x + 19y = 4 Datorming the integ 15
Find all solutions to the following Diophantine equations. i. 35x + 25y = 8 ii. 35x + 25y = 15 iii. 47x + 19y = 4 Datorming the integ 15
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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Modern applied algebra. Show work.

Transcribed Image Text:iii. 173 and 229
9. Prove that if n is odd, then gcd(3n, 3n + 2) = 1.
10. Find all solutions to the following Diophantine equations.
i. 35x + 25y = 8
ii. 35x + 25y = 15
iii. 47x + 19y = 4
11. Determine the positive integer solutions to 18x - 5y = 15.
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