Solve in integers :

$\large \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{12}$

Question

Solve in integers :

$\large \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{12}$

ganeshie8 · Answer

$\large   12x +12 y = xy  $

ganeshie8 · Answer

@mukushla

ganeshie8 · Answer

first obvious constraint :

12 | xy

anonymous · Answer

I thought you have the general solution for the equation you mentioned in the other post ;) i wanted to solve it with another method

ganeshie8 · Answer

Oh okay :) what is the other method ?

ganeshie8 · Answer

I have general solution only for `ax+by = c`

the xy term is throwing me off :/

anonymous · Answer

suppose $x<y$ there are some restrictions on $x$ and $y$ , for example $x$ must be less than 24 and greater than 12

miracrown · Answer

well, let's see if we can get y by itself
if we can solve for y = ... then we should be able to come to a better solution

anonymous · Answer

so u have $12<x<24$

miracrown · Answer

so you are right that we get 12x + 12y = xy next

anonymous · Answer

@Miracrown  i see the end of your solution, that will be nicer, neater than mine :-) let us do that and isolate one of the variables

anonymous · Answer

@ganeshie8  you see, we can put some restrictions on $y$ also

miracrown · Answer

so the first thing we want to do is solve for y
that means we need to get all the y-terms on the same side
so we move the x-term to the right hand side and xy to the left hand side:
so then we factor out the y and divide
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