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Not a fraction (Posted on 2011-04-11) Difficulty: 1 of 5
In what base is 41/14 an integer?

P&p(or just use your head),please.

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (3 votes)

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Solution P&P (spoiler) | Comment 1 of 3
a must be greater than 4.
(4a + 1)/(a + 4) is an integer

Let x = a + 4.  Then x must be greater than 8.
  
Then a = x - 4. Substituting,

(4x - 15)/x is an integer

So 15/x must be an integer.

So x must be 15.
a = x - 4 = 11

41 base 11 = 45, and 14 base 11 = 15, and 41/14 = 3


  Posted by Steve Herman on 2011-04-11 13:08:03
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