Proof analysis. The following is a proof to a theorem. Read the proof and state what the theorem is based on the structure of the proof. Proof: If gcd(a, b) = 1, then 1 = ax + by for some x, y; also c|a + 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:

Proof analysis. The following is a proof to a theorem. Read the proof and state what the theorem is based on the structure of the proof. Proof: If gcd(a, b) = 1, then 1 = ax + by for some x, y; also c|a + 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:

Name: Write the theorem statement here Proof analysis. The following is a pr
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Description: Write the theorem statement here Proof analysis. The following is a proof to a theorem. Read the proof andstate what the theorem is based on the structure of the proof.Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also c|a + b means a + b =

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Write the theorem statement here

Proof analysis. The following is a proof to a theorem. Read the proof and
state what the theorem is based on the structure of the proof.
Proof: If gcd(a,b) = 1, then 1 = ax + by for some x, y; also c|a + 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
%3D
Write the theorem statement here:

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