Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also cla + b means a + b = cr forsome integer r. Thus, b = cr - a, a = cr – b, so 1 = a(x – y) +c(ry) = b(y – x) + c(rx),which implies that gcd(a, c) = gcd(b, c) = 1.%3DWrite the theorem statement here:Now, rewrite the proof below giving explanations for each step along the way. Imagine youwere explaining this to someone. Justify each step.

Name: Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also cla + b
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Description: Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also cla + b means a + b = cr forsome integer r. Thus, b = cr - a, a = cr – b, so 1 = a(x – y) +c(ry) = b(y – x) + c(rx),which implies that gcd(a, c) = gcd(b, c) = 1.%3DWrite the theorem statem

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Proof: If gcd(a, b) = 1, then 1 = ax + by for some x, y; also cla + b mean some integer r. Thus, b = cr - a, a = cr - b, so 1 = a(x -y) + c(ry) = which implies that gcd (a, c) = gcd(b, c) = 1. %3D %3D %3D %3D Write the theorem statement here: Now, rewrite the proof below giving explanations for each step along the u were explaining this to someone. Justify each step.

Proof: If gcd(a, b) = 1, then 1 = ax + by for some x, y; also cla + b mean some integer r. Thus, b = cr - a, a = cr - b, so 1 = a(x -y) + c(ry) = which implies that gcd (a, c) = gcd(b, c) = 1. %3D %3D %3D %3D Write the theorem statement here: Now, rewrite the proof below giving explanations for each step along the u were explaining this to someone. Justify each step.

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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Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also cla + b means a + b = cr for
some integer r. Thus, b = cr - a, a = cr – b, so 1 = a(x – y) +c(ry) = b(y – x) + c(rx),
which implies that gcd(a, c) = gcd(b, c) = 1.
%3D
Write the theorem statement here:
Now, rewrite the proof below giving explanations for each step along the way. Imagine you
were explaining this to someone. Justify each step.

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