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?

Guest Feb 2, 2019

#1**+1 **

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.

Guest Feb 2, 2019

#2**+1 **

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

ElectricPavlov Feb 2, 2019