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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?

 Aug 4, 2021
 #1
avatar+34316 
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1a + 2   =   2b + 1    I'll switch to  use x and y

2y  = x+1

y = 1/2x + 1/2

    now solve for integers 

       when x = 3   y = 2    too small

       when x = 5   y = 3  

 

 

base 3     213 = 7

base 5    125  = 7                 7

 Aug 4, 2021
 #2
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0

thanks so much

Guest Aug 4, 2021

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