By adding 1 to the positive base N integer having the form XXXYYY with non leading zeroes, we get a perfect square- where X and Y are not necessarily distinct.

What are the value(s) of N, with 2 ≤ N ≤ 16, for which this is possible?

(XXXYYY_N + 1) is a perfect square where X = Y = (N-1).

In addition, where 2 <= N <= 16, the following are also perfect squares: 

111333₅
222666₉
111555₁₀
444888₁₀
333999₁₃
555888₁₆

Edited on April 26, 2009, 7:21 pm

Posted by Dej Mar on 2009-04-26 19:19:40