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# If x is a positive integer, is x! + (x + 1) a prime number?

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Manager
Joined: 13 Jun 2016
Posts: 107
Location: United States
Concentration: Finance, Technology
Re: If x is a positive integer, is x! + (x + 1) a prime number?  [#permalink]

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11 Aug 2016, 11:27
see 1 an 2 statements and then try to 2, 3 an 4 as examples. E
Manager
Joined: 20 Dec 2018
Posts: 50
Re: If x is a positive integer, is x! + (x + 1) a prime number?  [#permalink]

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21 Dec 2018, 20:52
Statement 1. x! + (x + 1)a might be a prime no if x is even depending on the value of a.
x! + (x + 1)a will not be a prime no if x >1 and odd because x! will be divisible by 2 and (x+1) will be even which will also be divisible be 2. Hence, Insufficient.
Statement 2. x is even. So, x! will be divisible by 2. Now, (x + 1)a will be divisible by 2 if ‘a’ is a prime no.Thus, x! + (x + 1)a won’t be a prime no if a is even.
And (x + 1)a will be odd if a is odd. So, x! + (x + 1)a might be prime if a is odd. Hence, Insufficient.
Statement 1 & 2 together. Combining the results of statement 1 & 2 together, we get,
x! + (x + 1)a will not be a prime no if ‘a’ is even.
x! + (x + 1)a might be a prime no if ‘a’ is odd.
Hence, Insufficient.
Re: If x is a positive integer, is x! + (x + 1) a prime number?   [#permalink] 21 Dec 2018, 20:52

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