Prove the identity:
for .
Proof. For the case

While, on the right we have,
So, the identity holds in the case . Assume then that it holds for some
. Then we have,
Hence, the statement is true for , and so, for all
This proof is wrong. When you multiply (1+ x^(2*m)).(1 – x^(2*m)) the result should be equals to (1-x^(4m))
No this is correct because it is not (1+x^(2*m)), but rather (1+x^(2^m)).