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interests / rec.puzzles / Re: 4 (positive) integers ... A, B, C, D

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

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From: emurph...@zoho.com (Edward Murphy)
Newsgroups: rec.puzzles
Subject: Re: 4 (positive) integers ... A, B, C, D
Date: Sun, 26 Jun 2022 13:41:07 -0700
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by: Edward Murphy - Sun, 26 Jun 2022 20:41 UTC

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)?

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

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Subject: Re: 4 (positive) integers ... A, B, C, D
From: henha...@gmail.com (henh...@gmail.com)
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by: henh...@gmail.com - Sun, 26 Jun 2022 21:23 UTC

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.

Subject	Author
Re: 4 (positive) integers ... A, B, C, D	Edward Murphy
Re: 4 (positive) integers ... A, B, C, D	henh...@gmail.com