# How does this imply this (number theory)

so I have
$$2^{1990}=(199k+2)^{10}$$
expanding I have.
$$2^{1990}=2^{10}+10.2^9. (199k)+\frac{10.9}{1.2} 2^8.(199k)^2+...+10.2. (199k)^9+(199K)^{10}$$-(1)

now its clear $$199|2^{1990}-2^{10}$$ since I can take 199 out of the RHS.

but the book seems to imply that the above equation(1) says $$10|2^{1990}-2^{10}$$ , but how?I cant see how the equation above says the $$10|2^{1990}-2^{10}$$ is true..

Thanks.