Have a look at these special numbers: 1233 and 990100. Do you notice anything special in these numbers?
Yes, these numbers are out of the ordinary indeed. If you break such numbers into two equal parts and add their squares, you recover the same number.
1233 = 12^2 + 33^2
990100 = 990^2 + 100^2.
Can you find an eight-digit number N with the same property, namely that if you break N into two four-digit numbers B and C, and add their squares, you recover N?
(N really has to have eight digits; its leading digit is not zero. B is the number formed by the first four digits of N, and C is the number formed by the last four digits of N.)
This puzzle is taken from Ponder This Challenge of IBM