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Kainui
If I know that a and b are integers, how would I prove that a=b in the equation ab=a+b?
i dont understand that question - the only values i can think of to fot satisfy it is if a and b wre both = 2
Or 0, I suppose I'm just curious how to come to this conclusion logically rather than just guessing.
see if this helps or not\[b=\frac{a}{a-1}=1+\frac{1}{a-1}\]from here show that\[a=b=2\]
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
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 :)
Oh...man :) ur very welcome my friend :)
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?
sure.. i'll look at this later...
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.