Jacobi's Two Square Theorem: The number of representations of a positive integer as the sum of two squares is equal to four times the difference of the numbers of divisors congruent to 1 and 3 modulo 4.
I find this on Google , but not able to find any proof . I have brute force it and find that this is correct. Can anyone tell me any proof or whether any test case on which this theorem fails. Really needed please help.