Question

If d = gcd(a, b), then a/d and b/d are relatively prime. To show this, let x and y be integers such that ax + by = d. Then (a/d)x + (b/d)y = 1, and so gcd (a/d, b/d) = 1. Use this to make a proof with more formal statements and details. You must specifically explain in your proof how (a/d)x + (b/d)y = 1 implies gcd(a/d, b/d) = 1.

Name: if d gcd a b then ad and bd are relatively prime to show this let x and y be integers such that ax by d then adx bdy 1 and so gcd ad bd 1 use this to make a proof with more formal statements 21195
Uploaded: 2022-09-09T06:05:06-08:00
Duration: 3 min 4 s
Channel: Adi S
Description: if d gcd a b then ad and bd are relatively prime to show this let x and y be integers such that ax by d then adx bdy 1 and so gcd ad bd 1 use this to make a proof with more formal statements 21195

          If d = gcd(a, b),
then a/d and b/d are
relatively prime. To show this,
let x and y be integers such
that ax + by = d.
Then (a/d)x + (b/d)y = 1, and so gcd
(a/d, b/d) = 1.
Use this to make a proof with more formal statements and
details. You must specifically explain in your proof how (a/d)x +
(b/d)y = 1 implies gcd(a/d, b/d) = 1.

Added by Emily B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/09/2022

Step 1

This means we need to show that \( \gcd\left(\frac{a}{d}, \frac{b}{d}\right) = 1 \). Show more…

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If d = gcd(a, b), then a/d and b/d are relatively prime. To show this, let x and y be integers such that ax + by = d. Then (a/d)x + (b/d)y = 1, and so gcd (a/d, b/d) = 1. Use this to make a proof with more formal statements and details. You must specifically explain in your proof how (a/d)x + (b/d)y = 1 implies gcd(a/d, b/d) = 1.