Loading ...
Sorry, an error occurred while loading the content.

Two questions: Mirror sequence reference and 6n+11= square?

Expand Messages
  • billoscarson
    Hi all: I am doing some homespun research relative to the distribution of primes and am in need of some help on two items. Question 1: Is there a
    Message 1 of 2 , Feb 29, 2004
    • 0 Attachment
      Hi all: I am doing some homespun research relative to the
      distribution of primes and am in need of some help on two items.

      Question 1: Is there a published reference for the "mirror
      sequence" as it relates to the distribution of a finite set (3,5,7
      for example)of divisors along the full set of odd numbers
      1,3,5,7,9,11. . . to any odd k? I have googled around and done a
      university library search and found nothing. I understand the mirror
      sequence is used extensively in primality testing, so hopefully
      someone here can point me toward a reference.

      Question 2: Is there a way to determine if the function "6n+11" ever
      forms a perfect square for some n (n=1,2,3,4 etc to any m), other
      than trial and error? I have tried a few thousand n's with negative
      results, but thought I'd ask if there is a better way before I do a
      more exhaustive check.

      Thanks for your consideration. Bill
    • mikeoakes2@aol.com
      In a message dated 29/02/04 16:17:28 GMT Standard Time, ... Bill: I don t understand Question 1, but can address your Question 2. Suppose there is a solution:
      Message 2 of 2 , Feb 29, 2004
      • 0 Attachment
        In a message dated 29/02/04 16:17:28 GMT Standard Time,
        billroscarson@... writes:


        > Question 2: Is there a way to determine if the function "6n+11" ever
        > forms a perfect square for some n (n=1,2,3,4 etc to any m), other
        > than trial and error? I have tried a few thousand n's with negative
        > results, but thought I'd ask if there is a better way before I do a
        > more exhaustive check.
        >
        >

        Bill: I don't understand Question 1, but can address your Question 2.

        Suppose there is a solution: x^2 = 6*n+11.
        Then x^2 = 2 mod 3.
        But this is impossible, by enumerating the 3 possible cases:-
        x mod 3 x^2 mod 3
        0 0
        1 1
        2 1
        So there is no solution..

        In technical terms: "2 is a quadratic nonresidue mod 3".

        -Mike Oakes


        [Non-text portions of this message have been removed]
      Your message has been successfully submitted and would be delivered to recipients shortly.