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Re: polynomials can't give only primes - sci.math #54025
Posted:
Sep 6, 1996 1:42 AM
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Anil Ravindran Menon (armenon@top.cis.syr.edu) wrote:
: In article <9ICLB2BB@gwdu03.gwdg.de>, slucks@gwdu03.gwdg.de (Stefan Lucks ) writes:
: |> mmnuk@risc.uni-linz.ac.at (Michael MNUK) writes:
: |>
: |> >ME> Murray Eisenberg <murray@math.umass.edu> wrote: [...] or a reference to a
: |> >ME> proof: A polynomial with integer coefficients cannot have only prime
: |> >ME> values at all the integers.
: |>
In anycase, it has been proved that there is indeed an integral
polynomial that gives primes whenever it takes positive values.
I do not have an idea of the explicit form of the polynomial. Could
anyone enlighten me on this?
: |> >[ ... ] In general, some years ago I remember to have
: |> >seen the solution in a book by Riesel (or so). The booktitle was
: |> >something like Factorization and Primality Testing.
: |>
: |> Hans Riesel, "Prime Numbers and Computer Methods for Factorization"
: |> Birkhaeuser: Boston, Basel, Stuttgart, 1985;
: |> ISBN 3-7643-3291-3 (Stuttgart, ...)
: |> ISBN 0-8176-3291-3 (Boston)
: |> Stefan
: |>
: |> Stefan Lucks Institut f"ur Numerische und Angewandte Mathematik
: |> Lotzestra\3e 16-18 37083 G"ottingen Germany
: See Hall & Knight Vol II (The title is "Higher Algebra" or some such thing). The proof
: is quite trivial.
: --arm
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