Quadratic Expression and Primes
Number Theory
Level
pending
Let x=p^2-3p+2 for all p is a prime greater than 3.Then the set of vales of x for all p is always divisible by how many no. of primes?
The answer is 2.
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1 solution
Splitting the equation x = ( p − 1 ) ∗ ( p − 2 )
It is safe to assume that since p > 3 any value of p will make p − 1 have 2 as a factor.
Coming to p − 2 unit place values that can be taken by p are odd and subtracting 2 from an odd prime will result in a number having factors of prime number other than 2 always.
Hence the minimum number of primes that can divide x is 2 .