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Ring isomorphism

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(See attached file for full problem description)

Z2 means modulo 2 and Z2n means modulo 2n.

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Solution Summary

This is a proof regarding a ring isomorphism.

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Proof:
I use Z_2 to represent Z2 and Z_2n to represent Z2n. Because this notation makes things clear.
So Z_2={0,1}, Z_2n={0,1,2,...,2n-1}.
"=>": If there is a ring homomorphism f from Z_2 to a subring in Z_2n, then ...

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