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Re: [PrimeNumbers] Two questions: Mirror sequence reference and 6n+11= square?

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  • 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 1 of 2 , Feb 29, 2004
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      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


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