IBM Ponder This #023 · March 2000

Let's borrow notation from LaTeX and let "^" denote exponentiation, so that x^2 means "x squared".

Consider the numbers 1233 = 12^2 + 33^2, and 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 our digits of N, and C is the number formed by the last four digits of N.)

Solution

Best opened after a real attempt

To be added.