Divisibility
Posted: Wed Jan 03, 2018 9:04 pm
Prove that any integer of the form ( 4k + 3 ) has a prime factor of the same form .
Any prime number greater than $2$ is in form $4k+1$ or $4k+3$.
So,if we multiply some $4k+1$ type primes,we will get 4k+1 type compsite number.So,we will get a $4k+3$ type integer if at least one prime factor of it is in $4k+3$ form.
So,we are done.