Let S = {1,5,9, 13, 17, …..} be the set of positive integers of the form 4k+1. An element p of S is an S-prime if p > 1 and the only elements of S that divide p are 1 and p. (For example, 9 and 49 are S-primes.) An element of S that is not 1 or an S-prime is an S-composite. (For example, 25 = 5 × 5 is an S-composite.) (i) Use strong induction to prove that every S-composite can be expressed as a product of S-primes. (ii) Give an example of an S-composite that can be expressed as a product of S-primes in more than one way.