(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 unit’s digit is divided by the tens digit.

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

Let a = tens digit, b = ones digit

The two equations for n can be combined to read:

10a + b = ab + 4b/a

or

b = 10a²/[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