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2.What is the smallest base-10 integer that can be represented as AA_5 and BB_7, where A and B are valid digits in their respective bases? 

 Feb 2, 2019
 #1
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A  A(base 11)
[11^1 x 10] + [11^0 x 10] =120
120_5 =35 - the smallest base 10 number.

 

B B(base 12)
[12^1 x 11] + [12^0 x 11] =143
143_7 =80 - the smallest base 10 number.

 Feb 2, 2019
 #2
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Is that   AA in base 5    and BB in base 7 ?

           11 in base 5 = 6  in base 10          11 in base 7 = 8 in base 10

 

If you are looking for the SAME number, I think   24 in base 10 is represented by   44 in base 5    and 33 in base 7

 Feb 2, 2019

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