(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?

 

Analytical solution boils down to

 SOLVE

bm+n= mn+4m/n b is the base

substitute t=n/m and solve for t= 1,2,3,4

you will get al the couples m.n for b<10

 

Posted by Ady TZIDON on 2007-09-17 12:56:41