A community for students.
Here's the question you clicked on:
 0 viewing
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?
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?

This Question is Closed

cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0i dont understand that question  the only values i can think of to fot satisfy it is if a and b wre both = 2

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0Or 0, I suppose I'm just curious how to come to this conclusion logically rather than just guessing.

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.3see if this helps or not\[b=\frac{a}{a1}=1+\frac{1}{a1}\]from here show that\[a=b=2\]

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.1aba=b a(b1)=b a=b/(b1) a would be integer, satisfied if numerator (b) is 0 or denominator (b1) is 1

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0Ah 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 noninteger answers. Cool.

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.1thanks for medal, my teacher @mukushla :)

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.3Oh...man :) ur very welcome my friend :)

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0If 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?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.3sure.. i'll look at this later...

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0Haha 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.