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A base-10 integer n can be represented as 32_a in one base and 23_b in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?

 Jun 10, 2020
 #1
avatar+110074 
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I'd do it like this

2+3a=3+2b

3a-2b=1

One solution is a=1 and b=1  (these are not real solutions yet but they work for this equation.

 

3(1)-2(1)=1

3(1+2t)-2(1+3t)=1        here I have added 6t and then taken it away again.

 

t 1 2 3 4
a=1+2t 3 5 7 9
b=1+3t 4 7 10 13

 

Now you can answer it.

 Jun 11, 2020
 #2
avatar+110074 
0
 Jun 11, 2020

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