so in this problem i no that gcd(a,n)=1 and the question i need to answer is : let p be any prime factor of n and let k be the number of times that p appears in the prime factorization of n. prove that φ(n/p^K) is even

so far i have

If p is prime, then φ(p^k) = p^(k-1)(p-1). So, if p is odd, then p-1 is even, hence

φ(p^k) is even.

There is an odd prime q, such that q^k appears in the prime factorization of n.

Then (q - 1)/φ(q^k)/φ(n). Hence φ(n) is even.

how can i finish answering the question