Verify the following:(a) For any positive integer n, ,Jn:::; <f>(n) :::; n.[Hint:Writen
Chapter 7, Problem 7(choose chapter or problem)
Verify the following:(a) For any positive integer n, ,Jn:::; (n) :::; n.[Hint:Writen = 2k0p1 pr,so (n) = 2k0-1pil. pr-1(pi - 1) (Pr -1).Now use the inequalities p - 1 > .JP and k - k/2 to obtain (n) 2k0-1 kJ/2 kr /2 Pi ] Pr (b) If the integer n > 1 has r distinct prime factors, then (n) n /2r.( c) If n > 1 is a composite number, then (n) :::; n - ,Jn.[Hint: Let p be the smallest prime divisor of n, so that p :::; ,Jn. Then(n) :::; n(l -1/ p).]
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