Prove that there is no such that .

* Proof. * Suppose otherwise, that there is some rational number

such that

. Then, since

, we know there exist integers

not both even (

I.3.12, Exercise #10 (e) such that

. Then, since

we have

But, by I.3.12, Exercise #10 (d), we know implies both and are even, contradicting our choice of and not both even. Hence, there can be no such rational number

*Related*

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