perplexus.info :: Just Math : Not a fraction

Not a fraction (Posted on 2011-04-11)

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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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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