(I) Determine all possible base ten 8-digit perfect square(s) N, with no leading zeroes, such that the number obtained by increasing the second digit (reading left to right) of N by 1 is also a perfect square.

(II)Determine all possible base ten 4-digit perfect square(s) N, with no leading zeroes, such that the number obtained by inserting two zeroes between the thousands digit and the hundreds digit of N is also a perfect square.

**** Calculators are allowed, but no computer programs.

(I)
24502500 = 4950² :: 25502500 = 5050²
38564100 = 6210² :: 39564100 = 6290²

(II)
2704 = 52² :: 200704 = 448²
7569 = 87² :: 700569 = 837²

Edited on October 27, 2011, 10:22 pm

Posted by Dej Mar on 2011-10-27 12:32:53