what is the value of gcd(a^2+b^2, a + b) if a and b are relatively prime?
Added by Miguel A.
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We need to find the greatest common divisor (gcd) of two expressions: \(a^2 + b^2\) and \(a + b\), given that \(a\) and \(b\) are relatively prime. Two numbers are relatively prime if their gcd is 1. Show more…
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What can you conclude about gcd(a, b) if there are integers s, t such that as + bt = 8? Wouldn't the answer be all linear combinations of a and b consisting of all the multiples of gcd(a,b) which is equal to 8? I do not understand some people are getting factors of 8 instead of multiples
Adi S.
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.
Discrete math! If a,b are two distinct prime numbers, then the GCD of a and b is?
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