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+1
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avatar+26 

What is the smallest base-10 integer that can be represented as $12_a$ in one base and $21_b$ in another base, where $a$ and $b$ are any bases larger than 2?

 Dec 22, 2023
 #1
avatar+126665 
+1

1a  + 2  = 2b + 1

 

1 =  2b - a                                            

 

Let a =  5 , b = 3         

 

125 =  213

 

1(5) + 2 =   2(3) + 1

 

7  =  7

 

cool cool cool

 Dec 22, 2023
 #2
avatar+26 
+1

Thank you so much!

Can you help me solve the other problem I posted about the 52 cards?

 Dec 22, 2023

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