a) Using Euclidean algorithm, find the gcd(101,4620) and express it as linear combination of the divisor...

Transcribed Image Text:

a) Using Euclidean algorithm, find the gcd(101,4620) and express it as linear combination of the divisor and the dividend. (7.5 Marks) b) If k + 1 integers are selected from the set {1,2,3,....,2k), where k is a positive integer, must at least one of them be odd? Justify your answer. (2.5 Marks) c) Proof the expression (+¹)=(2₂) + () where n and r be positive integers with r≤n. d) Using the expression in (c), find the value of (₂) and (3). (6 Marks) (4 Marks) a) Using Euclidean algorithm, find the gcd(101,4620) and express it as linear combination of the divisor and the dividend. (7.5 Marks) b) If k + 1 integers are selected from the set {1,2,3,....,2k), where k is a positive integer, must at least one of them be odd? Justify your answer. (2.5 Marks) c) Proof the expression (+¹)=(2₂) + () where n and r be positive integers with r≤n. d) Using the expression in (c), find the value of (₂) and (3). (6 Marks) (4 Marks)

Answer rating: 100% (QA)

Answer A The Euclidean algorithm is a method for finding the greatest common divisor GCD of two integers Heres how to use it to find the GCD of 101 an... View the full answer