Math Is Fun Forum

Keall

Member

Registered: 2008-08-18

Posts: 1

Integer algebra

You choose three POSITIVE integers: x, y and z.
The quotients                 1. (x*y)/(x+y)
                                    2. (x*z)/(x+z)
                                    3. (y*z)/(y+z)
shall also be integers.
So, then one has to prove the integers x, y and z have a factor in common which is bigger than 1.

The problem is that I absolutely don't know how to prove this.

Last edited by Keall (2008-08-18 23:46:21)

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Integer algebra

Interesting. Like it.
I'll give a hunt.

For a

to be an integer it must be that {x,y} is a solution to the diopantine equaiton

First let's investigate this diophantine: Let

So the general solutions of (1) in integers are:

Try to continue from here.

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