Provide a Proof for the following proposition and plese expl

Provide a Proof for the following proposition and plese explain each step! I\'ve seen other examples that they multiply 2 by 2n+1 can you explain why? also, why do we subtract them from each other?

Let a be an integer. If there exists an integer n such that al(4n 3) and al(2n 1), then a 1 or a 1. (Hint: Use the fact that the only divisors of are 1 and -1) 1

Solution

a|2n+1

Hence, a|2*(2n+1)

2*(2n+1)=4n+2

Hence, a|4n+2 and a|4n+3

This is only possible if a=1 or -1