$x^b-1$ and $x^b+1$ in different bases

Question

I'm a designer doing a project on numbers expressed in different base systems and am wondering why I'm running into so many prime factors ending in $1$. Here are $4$ conjectures I've created as a result of my playing. Any explanations as to why this is happening would be much appreciated.

x=any whole number

b=any base number (example: when $b=2$ answer is written in binary, when $b=7$ answer is written in base $7$, when $b=37$ answer written in base $37$, and so on)

For both $x^b-1$ and $x^b+1$:

1. will always result in largest prime factor $>x+1$ ending in the number $1$.
2. if $b$ is prime, all prime factors $>x+1$ will end in $1$.

Only for $x^b+1$:

3. if $b$ is any power of $2$, then all prime factors except $2$, will end in $1$.

Only for $x^b-1$:

4. if $b=2$*prime, all prime factors $>x+1$ will end in $1$.