Two questions: Mirror sequence reference and 6n+11= square?
- 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
- In a message dated 29/02/04 16:17:28 GMT Standard Time,
> Question 2: Is there a way to determine if the function "6n+11" everBill: I don't understand Question 1, but can address your Question 2.
> 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.
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
So there is no solution..
In technical terms: "2 is a quadratic nonresidue mod 3".
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