Every integer has a unique prime decomposition. Suppose for a moment that every prime factor was in fact not of the form 4k+3 (3 mod 4). There are only two kinds of primes, 2 and odd ones. Clearly an integer of the form 4n +3 is odd and thus does not have 2 as a factor. Thus every factor must be odd which leaves integers of the form 4k + 3 and 4l + 1 to make up its prime factorization (3 or 1 mod 4 respectively) . If one is of the form 4k + 3, you are done. So all must be of the form 4l + 1 (1 mod 4). Think about what happens when you multiply two numbers of this form together to see why this could never be the prime factorization.