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If  and  are positive integers, find A*B given that

 

(AB)_9 + A_9 = B0_9

 

Express your answer in base 10 (you do not need to include the subscript).

 Oct 5, 2018
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A and B must be integers in the range 0 to 8  (I'll assume here that A and B are both non-zero)

 

AB_9  is   9A+B

B0_9  is   9*B+0

 

So    9A+B + A = 9B + 0   or  10A = 8B

 

The only combination of integers in the range 1 to 8 that satisfy the above equality is A = 4 and B = 5, so A*B = 20 (in base 10).

 Oct 5, 2018
edited by Alan  Oct 5, 2018

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