Path: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!panix!.POSTED.panix1.panix.com!not-for-mail
From: "Keith F. Lynch" <kfl@KeithLynch.net>
Newsgroups: rec.puzzles
Subject: Re: Three rational triples
Date: Thu, 19 Sep 2024 12:16:57 -0000 (UTC)
Organization: United Individualist
Message-ID: <vch4np$lv$1@reader1.panix.com>
References: <vbs1kg$9ad$1@reader1.panix.com> <vcfkrh$qeo$1@reader1.panix.com> <60e28add10c8ff75a90697397ee0ba6f@www.novabbs.com>
Injection-Date: Thu, 19 Sep 2024 12:16:57 -0000 (UTC)
Injection-Info: reader1.panix.com; posting-host="panix1.panix.com:166.84.1.1";
	logging-data="703"; mail-complaints-to="abuse@panix.com"
X-Newsreader: trn 4.0-test77 (Sep 1, 2010)
Bytes: 1898
Lines: 32

HenHanna <HenHanna@dev.null> wrote:
> Keith F. Lynch wrote:
>> Since it's been more than a week, and nobody has figured it out:
>> Each of them has a sum that's equal to its product and is an integer.

> i think one person said exactly that.

Who and when?  I didn't see any such post.

> Is it easy to find them?

No, even though there are infinitely many.  Try and find one I
didn't list.

Constraints:  All three numbers must be positive, real, and rational,
but not integers.

And of course have to be in simplest form, i.e. 1/2, not 2/4.  One
person posted "52/39, 7/6, 9/2" which is of course the same three
numbers as my "9/2, 4/3, 7/6".  And he didn't say what property
they had, anyway.

Without any constraints, x,i,-i is always a solution for any x,
if i is the square root of minus one.

> How about 2 numbers

Too simple to be interesting.  If you want two numbers to have a sum
of S and a product of P, whether or not S=P, the two numbers will be
S + sqrt(S^2 - 4P) and S - sqrt(S^2 - 4P).
-- 
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.