# Why GCD(1+D, 1+D^2) = 1+D?

I'm reading Digital Communications, Proakis, and in order to classify an encoder as catastrophic or noncatastrophic I need the GCD of the elements in the generator G(D).

I don't really know what kind of math is being used, but does not seem as simple polynomial gcd to me.

It's not urgent, thanks!

It is polynomial math but the field is not the real (or complex) number field but rather the binary field GF$(2)$ in which addition and multiplication are done modulo 2. Hence, $$(1+D)^2 = 1 + 2D + D^2 \equiv 1 + D^2 \bmod 2$$ showing that $1+D$ divides $1+D^2$ (modulo 2) and so their greatest common divisor is just $1+D$ as claimed.