Thread: Combinatorial Study of Phi(n)
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Old November 5th, 2009, 11:13 AM
tonio tonio is offline
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Originally Posted by harkapobi View Post
Hi, I dont understand how you use this formula for \phi(m) to find m for question 2. Could you please explain a little further?

Katy

I'll give you a little additional hint: if n=p_1^{r_1}\cdot...\cdot p_k^{r_k}\,,\,\,then\,\,\phi(n)=p_1^{r_1}\cdot...\cdot p_k^{r_k}\left(1-\frac{1}{p_1}\right)\cdot...\cdot \left(1-\frac{1}{p_k}\right) =p_1^{r_1-1}\cdot...\cdot p_k^{r_k-1}(p_1-1)\cdot...\cdot (p_k-1).

OTOH, we know 12=2^2\cdot 3, so...

Tonio
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