n is a prime number.
Prove :
Since is odd we have that and are consecutive-evem numbers -they differ in 2-, so one of them must be divisible by at 2 -and not 4- and the other divisible by at least 4, thus, since , we must have that is a multiple of 8.
On the other hand, since 3 doesn't divide - because n is a prime greater than 4 - either or for some k in thus or hence
Now, since 3 and 8 divide , and 3 and 8 are coprime, then i.e.