(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?

part A:    28, 39 ,   

 

part B:

26 (BASE 9)=24(BASE 10)=2*6+4*6/2

24 (BASE 6)=16(BASE 10)=2*4+4*4/2

no analysis needed-  too few obvious candidates

may be there are other solutions as  well

 

Edited on September 17, 2007, 11:57 am

Posted by Ady TZIDON on 2007-09-17 11:30:00