Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: ilan_no_spew@hotmail.com (IlanMayer) Newsgroups: rec.puzzles Subject: Re: Pythagorean Primitives Date: Fri, 20 Jun 2025 17:24:45 +0000 Organization: novaBBS Message-ID: References: <103352u$l35p$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Info: i2pn2.org; logging-data="1319234"; mail-complaints-to="usenet@i2pn2.org"; posting-account="/bzfWjrXouyMv/K1i0HyE7gHQ6FRCGbCKFyL0OTWA1Y"; User-Agent: Rocksolid Light X-Spam-Checker-Version: SpamAssassin 4.0.0 X-Rslight-Posting-User: 560ba7e6d10b5b2973e51a7dc6b3f223c29b849b X-Rslight-Site: $2y$10$0RyD86brHnG2Dycc2W6RWO8ZhfDfP6cVQV19WE.tJoAnp.AIavHX2 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. SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER SPOILER 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 __/\__ \ / __/\\ //\__ Ilan Mayer \ / /__ __\ Toronto, Canada /__ __\ || --