Euler's Totient/Phi Function (step 4)

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Euler's Totient Function (also Euler's Phi Function)
  1. Art of the Problem
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Комментарии
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Very nice, but there is a minor inaccuracy in the video. The phi function is multiplicative, but the definition of multiplicative states that phi(a*b)=phi(a)*phi(b) if a and b are relatively prime (that is, gcd(a, b)=1). We can check that the rule is not true in general by looking at the example from the video: phi(8)=4. If the given multiplication rule held for all numbers then But since 2 is prime phi(2)=1. Which would imply that phi(8)=1.

jaystryker
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Thanks Jay. I'll add an annotation to remind people of this in case they are thinking about situations when gcd(a, b) != 1

ArtOfTheProblem
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Great vid! Clearly explained as always.

Cinqmil
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Thanks, nearly effed up all my homework! Still a great vid though.

cortez
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whoa lost me there? phi(8) = 4, phi (7) = 6? wouldn't phi(7) = 1? or phi(8) = 7?

Conor.Mcnuggets