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Re: seeking numerical example

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  • Kermit Rose
    ... Given that 10 = 3^2 + 1, I require that x1 x2 - y1 y2 = 1 and x1 y2 + x2 y1 = 3 and x1^2 + y1^2 = 5 and x2^2 + y2^2 = 2 This gives possible solution x1 =
    Message 1 of 4 , Mar 11, 2012
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      On 3/11/2012 9:03 AM, primenumbers@yahoogroups.com wrote:
      > 1c. Re: seeking numerical example
      > Posted by: "Maximilian Hasler"maximilian.hasler@... maximilian_hasler
      > Date: Sat Mar 10, 2012 9:37 am ((PST))
      >
      > On Sat, Mar 10, 2012 at 1:31 PM, Maximilian Hasler
      > <maximilian.hasler@...> wrote:
      >> > On Sat, Mar 10, 2012 at 12:10 PM, Kermit Rose<kermit@...> wrote:
      >>> >> Suppose we wish to look at the special subset of form { z such that z =
      >>> >> (t^2 + 1) = p q, where t is integer, and p and q are primes.}
      >> >
      >> > depending on the size of the numbers,
      >> > I think it's faster to consider products of primes and check whether
      >> > pq-1 is a square.
      > forprime(p=1,999,forprime(q=1,p,issquare(p*q-1)&print1(p*q",")))
      > 10,26,65,145,82,901,122,2501,2117,1157,485,5777,226,10001,1937,785,6401,362,20737,4097,3601,626,12997,18497,1765,10817,75077,111557,70757,842,64517,2305,81797,2705,7397,266257,1226,37637,23717,254017,11237,3365,320357,9217,144401,448901,1522,3845,207937,276677,60517,270401,527077,244037,104977,38417,712337,698897,
      >
      > This (in increasing order) is oeis.org/A144255 : semiprimes of the form n^2+1
      >
      > Maximilian


      Given that 10 = 3^2 + 1,

      I require that

      x1 x2 - y1 y2 = 1

      and

      x1 y2 + x2 y1 = 3

      and
      x1^2 + y1^2 = 5

      and

      x2^2 + y2^2 = 2

      This gives possible solution

      x1 = 2, y1 = 1, x2 = 1, y2 = 1


      Ok. Thank you Max.

      It appears that I have incompletely analyzed the requirements.

      I might or might not get back to you on this problem depending on
      my success in more completely analyzing the requirements of it.

      Kermit
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