How many different ordered pairs of positive integers are there each of whose squares sum to 9797 ? For example, for this ordered pair of positive integers, $$\((10,11)\)$$, its squares sum to $$\(10^{2}+11^{2}=221\)$$. [Hint: The identity $$\(\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)=(a c+b d)^{2}+(a d-b c)^{2}\)$$ can help.]

Answer:

Knowledge points:

Solution: