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Subject: =?UTF-8?B?UmU6IFLDqXNvdWRyZSBjZXR0ZSDDqWdhbGl0w6k=?=
Date: Mon, 5 Jun 2023 22:40:56 +0200
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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).



-- 
Fabrice