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#1**+2 **

[ 8(a) + b ] + 5[ a + b] = 13a + 6b

13a + 6b = 8b + a

12a = 2b

6a = b

a cannot be an integer > 1 because this would make b at least 12....which is impossible in base 8

So...

a = 1 and b = 6

Proof

16_{8} + 5 [ 1 + 6] = [ (1)*8 + 6] + 5*7 = [ 14 ] + 35 = 49

And

61_{8} = 6(8) + 1 = 49

So

N = 16_{8}

_{ }

CPhill Mar 14, 2019

#2**-1 **

Oh, I see. I thought we had to add the digits when solving in base 8, so I got really confused. Thanks a lot for your help!!! I like the proof!

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Mar 14, 2019