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I have 3 numbers and product of any 2 is equal to 3rd one. Is it true that 3 numbers must be either all 0's or all 1's?

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I have 3 numbers and product of any 2 is equal to 3rd one. Is it true that 3 numbers must be either all 0's or all 1's?
posted Jan 16, 2018 by Salil Agrawal

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2 Answers

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yes. It has to be either 0 or 1

answer Jan 16, 2018 by Thillairajan
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ab = c ----- 1
bc = a ----- 2
ca = b ----- 3

Sub 1 in 2
b(ab) = a
b^2 = 1 { assuming a is not equal to 0 }
b=+1,-1

Sub 2 in 3
c(bc) = b
c = +1,-1 { assuming a is not equal to 0 }
and also a = +1,-1.

ie a,b,c = +1,-1 & 0.

answer Jan 16, 2018 by Tejas Naik



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