a. Use the unique factorization theorem to answer the following question: If the prime f...

a. Use the unique factorization theorem to answer the following question: If the prime factorization of an integer n contains k occurrences of a prime number p, how many occurrences of p are contained in the prime factorization of ?

b. An alternative proof of the irrationality of counts the number of 2's on the two sides of the equation and deduces a contradiction. Write a proof that uses this approach.