1) 
A difference of identical powers of two numbers is divided without a remainder by a difference of these two
numbers, i.e. x^{m} a^{m}< is divided by ( x a ).

2) 
A difference of identical even powers of two numbers is divided without a remainder both by a difference
and by a sum of these two numbers, i.e. if m an even number, then the binomial x^{m} a^{m} is divided both ( x a ) and by
( x + a ).
A difference of identical odd powers of two numbers isnt divided by a sum of these two numbers.

3) 
A sum of identical powers of two numbers is never divided by a difference of these two numbers.

4) 
A sum of identical odd powers of two numbers is divided without a remainder by a sum of these two numbers.

5) 
A sum of identical even powers of two numbers is never divided both by difference and by a sum of these two numbers.
