This was an old question in a math competition which I couldn't figure out.
Suppose we have the following situation:
Person A chooses a four-digit natural number. Person B chooses a natural number and adds the square of it to the number chosen by A. Person C chooses a natural number and multiplies the square of it to the number chosen by person A. Then the results of B and C is multiplied and the result is 123456789. What number did A choose?
For clarity: Let the number chosen by A be a, the number chosen by B be b, and the number chosen by C be c. We then have:
$$(b^2 + a)(c^2\cdot a)= 123456789.$$
How would you solve this problem without a calculator?