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 In every numeration system (base b) there is a three-digit integer that is (b+1)  times the sum of its digits. In base ten the number is 198. In base three the number is 121. Find the number in base seven that has this property

Guest Feb 11, 2018
 #1
avatar+92816 
+1

8 * (a + b + c)  =  49a + 7b + c

 

8a + 8b + 8c =  49a  + 7b + c

 

41a - b - 7c  = 0

 

41a  - b  =  7c

 

a  =  1

b = 6

c = 5

 

1657

 

Proof

 

8 ( 1 + 6 + 5 )  =  1(7)^2  + 6(7)  + 5

 

8 * 12   =   49    +  42   + 5

 

96  =  49 + 47

 

96  =  96

 

 

cool cool cool

CPhill  Feb 11, 2018
 #2
avatar+77 
+1

This question is really intresting. I solved it myself recently.

neurolover25  Feb 12, 2018

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