A four digit number is squared to form an eight digit number. The center four digits of that square form the four digit number. Find all possible four digit numbers.

*(If 'abcd' was the four digit number, then the eight digit number would look like 'wxabcdyz'.)*

Easiest way I could think of solving this would be a simple programming
loop. The smallest 4 digit number yielding an 8 digit number is
3163 and the largest = 9999

using a simple C program which squared, trimmed, and compared I got only two answers (3792, 7600)