- #1

- 10

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[tex]2^{1990}=(199k+2)^{10}[/tex]

expanding I have.

[tex]2^{1990}=2^{10}+10.2^9. (199k)+\frac{10.9}{1.2} 2^8.(199k)^2+...+10.2. (199k)^9+(199K)^{10}[/tex]-(1)

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

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

Thanks.