Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

prime number?

Let f(n) = ((4n-2)/(n+1))*f(n-1), n >1

Supposed f(2) and f(3) are prime numbers. Prove that f(n) is Not prime for any other integer values n>1.

How could I prove that?

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    it is a little difficult

    notice that f(3)=5/2 * f(2)

    and they are prime numbers,

    so f(2)=2 and f(3)=5

    f(4)=14 is not a prime number

    so we can define

    f(1)=1 and f(0)=1

    therefore

    f(n)=(4n-2)/(n+1)*f(n-1)

    =(4n-2)(4n-6)/(n+1)n*f(n-2)

    =............

    =(4n-2)...*6*2/(n+1)...*3*2 *f(0)

    =2^n*((2n-1)!!)/((n+1)!)

    each odd number in (n+1)!

    appear at least once in (2n-1)!!.

    when n>4,

    the power of 2 in (n+1)!

    is not more than n-2

    (need a simple proof).

    so (n+1)! divides 2^n((2n-1)!!)

    and the quotient can be

    divided by 4

    so f(n) is not prime for n>=4

    Source(s): Jessica http://www.tucia.com/
Still have questions? Get your answers by asking now.