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I'm really stuck on the following question. I understand logically why this makes sense, and I've read a few proofs on this site of the multiplicative property of Euler's Totient, but those all seem beyond the scope of my class. Is there a simple proof to address the following question?
Suppose a number m is the product of two distinct primes, p and q. prove that the Euler totient of m is equal to (p-1)(q-1). For instance, the Euler totient of 35 (which is 5 * 7) is equal to 4*6, or 24. But remember that when you prove a theory you need to write it in terms of variables rather than numbers. (hint: you might want to check additive or multiplicative properties of totient function)