Question

Find the solution where x and y are integers to:

1/x + 1/y = 1/14

I can use a computer to get a list of solutions:

7, -14
10, -35
12, -84
13, -182
15, -210
16, 112
18, 63
21, 42
28, 28

but I'm having trouble solving this analytically and coming to a general formula.

Answer 1

1/x + 1/y = 1/14

(x+y)/xy=1/14 Inverse

xy/(x+y)=14

xy=14x+14y



xy-14x=14y

x(y-14)=14y



xy=14x+14y

xy-14y=14x

y(x-14)=14x Divide with (x-14)

y=14x/(x-14)

Solutions:

x-14#0
and
y=14x/(x-14) x#0

Answer 2

Do not forget that, since x and y are symmetric, they are interchangeable on your list.

Example: if (13, -182) works, then (-182, 13) works as well.

Answer 3

Go to:
wolframalpha com

When page be open in rectangle type:
1/x + 1/y = 1/14
and click option =

When you see results couple times click option: More Solutions

Answer 4

bosnian, i already used wolfram alpha to get the solutions I listed. I want to derive the solution analytically.

anon, I believe you just did algebraic rearrangement.