Hi,
I am having difficulty with some proofs.
Show that every composite integer of the form 4n+3 has a factor of the form 4m+3.
and
Show that every composite integer of the form 6n+5 has a factor of the form 6m+5.
Hi,
I am having difficulty with some proofs.
Show that every composite integer of the form 4n+3 has a factor of the form 4m+3.
and
Show that every composite integer of the form 6n+5 has a factor of the form 6m+5.
I do this one.
Note the number is not even, so its prime factors are all odd. Hence they have the form . Note that if all prime factors had the form then their overall product also have the same form. Which is impossible because the number has the form . This means at least of these prime factors must have the form .