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Which of the following is (are) true if f(n)=the number of distinct primes that divide...

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christiano-cr7 | Salutatorian

Posted July 19, 2013 at 6:54 PM via web

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Which of the following is (are) true if f(n)=the number of distinct primes that divide n for n>1

(!)f(10)=f(12)

(!!)If f(n)>1,then f(f(n))<f(n)

(!!!)If f(n) = 3, then n<1000

A)All

B)(!)and (!!)only

C)(!) only

D)(!) and (!!!) only

E)None

 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 19, 2013 at 7:05 PM (Answer #1)

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`f(10)=f(2xx5)=2 . f(12)=f((2^2)xx3)=2` .So `f(10)=f(12)` .Clearly `f(n)<n` .Then `f(f(n))<f(n)` .So (!!) is true .But (!!!) is not true as we could let n be the product of three distinct primes greater than `1 000` .Then  ` n>1 000` but` f(n)=3`

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