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## Main Question or Discussion Point

I know it's a dumb question but I can't figure out why the totient of

n = p

phi(p

But why is it true in the general case? I think I could use multiplicativity of phi() to prove it but I am confused by the "follows from definition" note.

*n*is always even (I've read in a book that it "follows immediately from the definition of the totient function", so it should not require any theorem to prove). It is clear to me that it holds true forn = p

^{k}, where p is a prime, becausephi(p

^{k}) = p^{k - 1}(p - 1) and (p - 1) is evenBut why is it true in the general case? I think I could use multiplicativity of phi() to prove it but I am confused by the "follows from definition" note.