P&C Challenge 1

IIT JEE 2015 Preparation › Algebra questions › P&C Challenge 1

Let p be a prime number such that pâ‰¥11.Let n=p!+1. Find the number of primes in the list n+1,n+2,n+3,....,n+p-1..

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kaymant ·2009-10-15 21:41:14

There are no primes in the list.
For k=1,2,3,...,p-1, we have
n+k=p!+1+k
since k+1 can go up to p, it must be contained in p!, hence
n+k=p!+1+k = (k+1)q for some integer q. But that means n+k is composite.

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Rocky Crazy ·2009-10-15 21:50:59

Thanks Kaymant sir!!

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P&C Challenge 1

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