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 (n+1r)=(nr1)+(nr) where n and r be positive integers with rn (6 Marks) d) Using the expression in (c), find the value of (62) and (63). (4 Marks)