## Kainui 2 years ago If I know that a and b are integers, how would I prove that a=b in the equation ab=a+b?

1. cwrw238

i dont understand that question - the only values i can think of to fot satisfy it is if a and b wre both = 2

2. Kainui

Or 0, I suppose I'm just curious how to come to this conclusion logically rather than just guessing.

3. cwrw238

oh ok

4. mukushla

see if this helps or not$b=\frac{a}{a-1}=1+\frac{1}{a-1}$from here show that$a=b=2$

5. mukushla

and or$a=b=0$

ab-a=b a(b-1)=b a=b/(b-1) a would be integer, satisfied if numerator (b) is 0 or denominator (b-1) is 1

7. Kainui

Ah thank you very much I see. By making it in terms of fractions we eliminate the impossible solutions by seeing fairly obviously which values will give non-integer answers. Cool.

thanks for medal, my teacher @mukushla :)

9. mukushla

Oh...man :) ur very welcome my friend :)

:)

11. Kainui

If you're having fun, can we take this a couple steps further and look at how to show abc=a+b+c as all integers can only allow 0 or 1,2,3 as answers (in 3! ways). Since the extra variables are involved it gets a little trickier. Then I noticed I could extend these rules to n number of variables so that abcde=a+b+c+d+e would have answers of 0 or 1,1,1,2,5. But it might possibly have more. Anyone interested in playing around with this with me for fun?

12. mukushla

sure.. i'll look at this later...

13. Kainui

Haha alright. If you know any websites that talk about this or what this is called if it has a name, that would be extrodinarily helpful.