In continuation of 5 Digit Number, let us define a 5-digit non leading zero base N (N > 3) positive integer x as a split number whenever, 3*x is a perfect square and, when the digits of x are split, the first number is double the second one.

How many split numbers are there whenever 11 ≤ N ≤ 36. What are the respective minimum and maximum values?

(Splitting a base-N 5-digit number into two numbers means 12345 into 1 and 2345 or, 123 and 45.)

(In reply to A start. by Jer)

Huh?  Maybe I'm not following you, Jer, but this looks like a false start to me.

Edited on January 3, 2011, 8:25 pm

Posted by Steve Herman on 2011-01-03 17:16:55