Consider number 10. It has even number of divisors i.e., 10 has 4 divisors {1, 2, 5, 10}. Let n be a number having odd number of divisors. Let k be the middle element among the distinct divisors ordered according to increasing order.
(a) Prove that gcd(k + 1, n) = 1.

(b) Is the statement true even if n has even number of divisors with respect to the two middle elements? If Yes, prove your answer. Else give a counter example.