Show that for any integer $n>1$, all the numbers $n!+2, n!+3, \ldots, n!+n$ are composite (i.e. not prime).
Show that a number is not prime?
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number-theory
prime-numbers
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4Remember what the definition of the factorial is. – 2010-10-13
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0@maths student: Try to write out $n!+2, n!+3, ...$ for a small $n$ (say $n=4$). You should see it then. (Remember: $4! = 4*3*2*1$). – 2010-10-13
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0@Jens: Well n!=n*(n-1)! and n can only be written as n*1 since we are not told that it cannot be prime, So d=1 or n. But that's not helpful as any integer is divisible by 1 and obviously n! is divisible by n. What am I not seeing? – 2010-10-13
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0@maths student: You're seeing everything there is to see, I think. Since $n!$ and $n$ are both divisible by $n$, so is $n!+n$, and therefore it is not prime. That's what you wanted. =) – 2010-10-13
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0@Jens: Ah so I got it! Thank you!!! – 2010-10-13