Recent content by nelson98

Thank you very much for the help! I appreciate you working me through this.

Thanks for the hint! So, we've established that a|b, a|b, so a|b-c. b-c = (4n+3) - (2n+1) = (2n+2) Therefore, we know a|2n+1 and a|2n+2. These two are only one apart. Is that why a = +1 or -1?

So, I know K1=4n+3, where K is an integer, and I know K2=2n+1. But then, I have a, K1, and K2, and n, all of which are unkowns. How, then, do I solve for this?

Homework Statement Suppose that n is an odd integer. Prove that n is either one greater than a multiple of 4 or one less than a multiple of 4. Homework Equations N/A The Attempt at a Solution I realize that this is going to be a direct proof. However, I am stumped on where to...

Homework Statement For some integer n, a|(4n+3) and a|(2n+1). Therefore, 4n+3 is an integer multiple of a, as well as (2n+1). Prove or disprove that a=+/-1. Homework Equations N/A The Attempt at a Solution I have been working on this one for quite some time now, but I cannot...

Homework Statement Every triple of consecutive odd natural numbers, with the first being at least 5, contains at least on composite. Homework Equations N/A The Attempt at a Solution I know from number theory that of every set of consecutive odd integers, one of them is divisible...