Practice Lecture – 57: Properties Of Gcd And Bezout’s Theorem (9) - Lecture – 57: Properties of GCD and Bezout’s Theorem

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6 sample questions

Question 1.
What is the GCD of 24 and 36?
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Use the prime factorization method.
Question 2.
State Bezout’s theorem in your own words.
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Think about what linear combinations mean.
3Question 3.
What is Bezout's theorem?
- A method to find primes
- A theorem about GCD and linear combinations
- An algorithm to find the multiplicative inverse
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Think about what the theorem involves.
4Question 4.
True or False: The multiplicative inverse of a number a modulo N exists if and only if GCD(a, N) = 1.
- True
- False
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Consider the relationship between inverses and GCD.
Question 5.
Prove that for any integers a and b, there exist integers x and y such that ax + by = gcd(a, b).
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Use examples such as (252, 198) during your proof.
Question 6.
Given a = 13 and N = 24, find the multiplicative inverse modulo N.
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Use the extended Euclidean algorithm to compute this.

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