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Getting the Numbers With Product And Quotient (Posted on 2007-09-17) Difficulty: 3 of 5
(A) Analytically determine all possible two digit positive decimal integers n, that satisfy this equation:

       n = p + 4c

where p is the product of the digits of n, while c is the result when the unitís digit is divided by the tens digit.

(B) For what positive integer bases N< 10 do valid solutions to the above equation exist?

See The Solution Submitted by K Sengupta    
Rating: 1.5000 (2 votes)

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Solution Solution - Part (A) | Comment 5 of 7 |
Let a = tens digit, b = ones digit

The two equations for n can be combined to read:

10a + b = ab + 4b/a

or

b = 10a≤/[a(a+1) + 4]

Since a = {1,...,9}, substituting these values yields only one solution for b where b = {0,...,9}

a = 3, b = 9

n = 39

  Posted by hoodat on 2007-09-17 17:14:25
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