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  • REZA RANJBAR
    Let P(x) is none-zero polynomial on R (the set of all real number). Show that. There is none –zero polynomial K(x) which P(x)*K(x)=a(0) + a(1)x^2 +
    Message 1 of 4 , Sep 4 3:29 PM
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      Let P(x) is none-zero polynomial on R (the set of all real number).



      Show that.



      There is none �zero polynomial K(x) which



      P(x)*K(x)=a(0) + a(1)x^2 + a(2)x^3 +a(3)x^5 +a(4)x^7+ � a(n)x^p(n).

      for some p(n).

      Such that p(n) is nst. Prime number.

      Remark: a(i) is not zero for all i such that 0<=i<=n.



      Send me.thank you.



      Saeed ranjbar.



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    • richard042@yahoo.com
      ... number). ... Take any two univariate polynomials, P(x) and K(x), such that their orders sum to p(n), then yes, you can multiply them together to create a
      Message 2 of 4 , Sep 4 10:59 PM
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        --- In primenumbers@yahoogroups.com, REZA RANJBAR
        <saeedgeometr22@y...> wrote:
        > Let P(x) is none-zero polynomial on R (the set of all real
        number).
        > Show that.
        > There is none –zero polynomial K(x) which
        >
        > P(x)*K(x)=a(0) + a(1)x^2 + a(2)x^3 +a(3)x^5 +a(4)x^7+ … a(n)x^p(n).
        >
        > for some p(n).
        > Such that p(n) is nst. Prime number.
        > Remark: a(i) is not zero for all i such that 0<=i<=n.

        Take any two univariate polynomials, P(x) and K(x), such that their
        orders sum to p(n), then yes, you can multiply them together to
        create a new polynomial with order p(n).

        >
        > Send me.thank you.
        >
        > Saeed ranjbar.

        I think it's as simple as that, but perhaps I am missing something?

        Regards,

        -Dick
      • Edwin Clark
        ... It seems that Reza is not asking for just a polynomial of degree p(n), but a polynomial of the form a(0) + sum(a(i)x^p(i),i=1..n) where each a(i) is not
        Message 3 of 4 , Sep 5 9:10 AM
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          On Sun, 5 Sep 2004 richard042@... wrote:

          > --- In primenumbers@yahoogroups.com, REZA RANJBAR
          > <saeedgeometr22@y...> wrote:
          > > Let  P(x) is none-zero polynomial on  R (the set of all real
          > number).
          > > Show that.
          > > There is none –zero  polynomial    K(x)  which
          > >
          > > P(x)*K(x)=a(0) + a(1)x^2 + a(2)x^3 +a(3)x^5 +a(4)x^7+ … a(n)x^p(n).
          > >
          > > for some p(n).
          > > Such that  p(n) is nst. Prime number.
          > > Remark: a(i) is not zero for all i such that  0<=i<=n.
          >
          > Take any two univariate polynomials, P(x) and K(x), such that their
          > orders sum to p(n), then yes, you can multiply them together to
          > create a new polynomial with order p(n).

          It seems that Reza is not asking for just a polynomial of degree p(n), but
          a polynomial of the form a(0) + sum(a(i)x^p(i),i=1..n) where each a(i)
          is not zero and p(i) is the ith prime.

          Clearly you must rule out polynomials of the form P(x) = x^j*f(x)
          where j > 0 since that would force a(i) = 0 for i < j.

          But even if you make the assumption that x does not divide P(x) the
          result is not true. Take P(x) = 1 + x^2 + x^4. I claim
          that if P(x)K(x) has 0 coefficients for x^j when j > 0 and not prime
          then it will also have 0 coefficients for x^0 and x^2.


          Edwin
        • Cletus Emmanuel
          No homework requests please!!! REZA RANJBAR wrote: Let P(x) is none-zero polynomial on R (the set of all real number). Show that.
          Message 4 of 4 , Sep 7 7:02 AM
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            No homework requests please!!!

            REZA RANJBAR <saeedgeometr22@...> wrote:
            Let P(x) is none-zero polynomial on R (the set of all real number).



            Show that.



            There is none �zero polynomial K(x) which



            P(x)*K(x)=a(0) + a(1)x^2 + a(2)x^3 +a(3)x^5 +a(4)x^7+ � a(n)x^p(n).

            for some p(n).

            Such that p(n) is nst. Prime number.

            Remark: a(i) is not zero for all i such that 0<=i<=n.



            Send me.thank you.



            Saeed ranjbar.



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