1. Forum
  2. Usenet
  3. REC.PUZZLES

  • 4 (positive) integers ... A, B, C, D

    From henhanna@gmail.com@21:1/5 to All on Sun Jun 19 18:13:03 2022
    4 (positive) integers ... A, B, C, D

    such that the 6 (pairwise) differences are all squares.


    Are there more such 4-tuples ?

    Are there MANY more such 4-tuples ?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Edward Murphy@21:1/5 to henh...@gmail.com on Sun Jun 26 13:41:07 2022
    On 6/19/2022 6:13 PM, henh...@gmail.com wrote:

    4 (positive) integers ... A, B, C, D

    such that the 6 (pairwise) differences are all squares.


    Are there more such 4-tuples ?

    Are there MANY more such 4-tuples ?

    Given the assumption that at least one such 4-tuple exists (I haven't
    tried to find one), you should be able to derive infinitely many others
    by multiplying all four numbers by some square. The more interesting
    question is, how many such 4-tuples exist that can't be derived that
    way (i.e. the six differences have no square factor > 1 in common)?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From henhanna@gmail.com@21:1/5 to Edward Murphy on Sun Jun 26 14:23:45 2022
    On Sunday, June 26, 2022 at 1:41:12 PM UTC-7, Edward Murphy wrote:
    On 6/19/2022 6:13 PM, henh...@gmail.com wrote:

    4 (positive) integers ... A, B, C, D

    such that the 6 (pairwise) differences are all squares.


    Are there more such 4-tuples ?

    Are there MANY more such 4-tuples ?


    Given the assumption that at least one such 4-tuple exists (I haven't
    tried to find one), you should be able to derive infinitely many others
    by multiplying all four numbers by some square. The more interesting
    question is, how many such 4-tuples exist that can't be derived that
    way (i.e. the six differences have no square factor > 1 in common)?


    good question... (or good restatement)

    i'm curious about ........

    5 (positive) integers ... A, B, C, D , E
    such that the ... (pairwise) differences are all squares.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)