Minimize the bases P and Q such that each of the following alphanumeric equations has at least one solution:

(A) (GO)_{Base P} + (GO)_{Base P} = (GIG)_{Base P}

(B) (GO)_{Base Q}*(GO)_{Base Q} = (GIG)_{Base Q}

Note: Solve each of the alphanumeric equations separately and remember G, O and I must be distinct and G can't be zero.

(In reply to Analytical Soltuion by Gamer)

It is clear that prime Q (like 7) are not possible. However for other Q>7, there still may be solutions.

The goal is for there to be a multiple of Q in the form O^2-1 less than Q(Q-5).

Since O^2-1=(O+1)(O-1) it can be seen that we need some of the factors from Q to come from (O+1) and some to come from (O-1), but the remaining factors' product needs to be less than (Q-5). So looking for numbers of the form O^2-1 and their large factors gives a list for O and Q. From this, I can be computed and the solution determined.

Posted by Gamer on 2007-05-25 23:41:17