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For every positive integer x, f(x) represents the greatest prime fact

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Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

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New post 19 Jul 2019, 05:41
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For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2^x+1. What is (g(f(12))?

If f(x) represents the greatest prime factor of x!, the greatest prime factor of it will be 11.
---> (g(f(12))=g(11)=2^x+1=2^11+1=2048+1=2049

it says that g(x) represents the smallest prime factor of 2^x+1 (=2049)
--- > The smallest prime factor of 2049 is 3.

The answer choice is B.
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For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

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New post 19 Jul 2019, 05:57
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. What is (g(f(12))
(g(f(12))?

f(12) = largest prime factor of 12! which is 11
g(11) = smallest PF of 2^11+1 = 2049
so B. 3 is the answer

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Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

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New post 19 Jul 2019, 06:54
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x=12, f(x) is greatest prime factor of x!, so x! = 12! = 12x11x10.....x1, the greatest prime factor is 11 --> f(x) = 11
g(x) is smallest prime factor of 2^x+1, since x = f(x) = 11 --> g(x) = g(2^11+1)
2^11+1 is odd number (=2049), and the smallest odd prime number is 3, so g(2^11+1) = 3
Answer is (B)
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Re: For every positive integer x, f(x) represents the greatest prime fact  [#permalink]

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New post 19 Jul 2019, 07:53
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f(12) = Greatest Prime Factor of 12!, that is 11.

g(11)= Smallest Prime Factor of 2^11 + 1
2^11+1=32x32x2+1=2049, which is divisible by 3, so the smallest prime factor is 3.

There might be a better solution to avoid the calculation but this is the best I got.
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Re: For every positive integer x, f(x) represents the greatest prime fact   [#permalink] 19 Jul 2019, 07:53

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