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From: ilan_no_spew@hotmail.com (IlanMayer)
Newsgroups: rec.puzzles
Subject: Re: Pythagorean Primitives
Date: Fri, 20 Jun 2025 17:24:45 +0000
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On Fri, 20 Jun 2025 8:11:10 +0000, David Entwistle wrote:

> I hope this question is clear. If not, please suggest a change to make
> the
> intention clearer (assuming you can work the intention out)...
>
> Most of us are familiar with the (3, 4, 5) right-triangle. 5 is the
> smallest integer hypotenuse which supports two other sides of a right-
> triangle with integer length. There are many other right-triangles with
> integer sides, such as: (5, 12, 13) and (8, 15, 17). These triples are
> considered primitive as the terms do not share a common factor.
>
> On the other hand, although (6, 8, 10) is a right-triangle, it is NOT
> primitive as the elements share a common factor, 2.
>
> Can you find the first four terms in the series where a(n) is the least
> hypotenuse of which 2^(n-1) Pythagorean triples are primitive? So, 5 is
> the smallest and supports one triple. Can you find a hypotenuse that
> supports two discrete primitive Pythagorean triples, four and eight?
>
> Good luck.

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3 4 5

16 63 65
33 56 65

47 1104 1105
264 1073 1105
576 943 1105
744 817 1105

716 32037 32045
2277 31964 32045
6764 31323 32045
8283 30956 32045
15916 27813 32045
17253 27004 32045
21093 24124 32045
22244 23067 32045


Please reply to ilanlmayer at gmail dot com

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