Proving the Integer Multiples of A for (4n+3) and (2n+1): Homework Statement

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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 even start it right. Can somebody help me?
 

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