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Path: ...!3.eu.feeder.erje.net!feeder.erje.net!usenet.goja.nl.eu.org!pasdenom.info!from-devjntp Message-ID: <Qg1CoW0fH_bSpVyO9ewIQDfGiUU@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: =?UTF-8?Q?R=C3=A9soudre=20cette=20=C3=A9galit=C3=A9?= References: <zF0ezWzZVwyFPc1y2dkU7tlBpJg@jntp> <u5lh8p$65g$1@shakotay.alphanet.ch> Newsgroups: fr.sci.maths JNTP-HashClient: t9q6vzzIKiRGViFTyvi2ix4Q7jA JNTP-ThreadID: y5AARJZgCgK-TFGI3u9nMz3g4lY JNTP-Uri: http://news2.nemoweb.net/?DataID=Qg1CoW0fH_bSpVyO9ewIQDfGiUU@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 05 Jun 23 22:10:27 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/114.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="dedfcf59a7c832644f5463c41a9f790ecbb0a5e4"; logging-data="2023-06-05T22:10:27Z/7966970"; posting-account="4@news2.nemoweb.net"; mail-complaints-to="newsmaster@news2.nemoweb.net" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: Richard Hachel <r.hachel@tiscali.fr> Bytes: 1834 Lines: 17 Le 05/06/2023 à 22:40, robby a écrit : > Le 05/06/2023 à 21:20, Richard Hachel a écrit : >> (1/x)+(1/y)=(1/10) >> x et y entiers naturels. > > - il y a symétrie entre les solutions (x,y) et (y,x) > > - y = 1/ ( 1/10 - 1/x ) = 10x / ( x - 10 ) > donc x >= 10 et x doit diviser 10 : > x =: 10X → y = 10X / ( X - 1 ) > donc X-1 divise 10, donc = 1, 2, 5 ou 10 > > donc x = 20, 30, 6O ou 110 ( correspondant à y = 20, 15, 12, 11 ) > + symétrique (y,x). Non. R.H.