Suppose that all of

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,

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, and

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are distinct.

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,

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, and

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. Multiplying these all together yields

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.

Rearrange to get

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(possible since

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. Since

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is a polynomial with integer coefficients,

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. Since their product is one,

If one of

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,

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, and

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is -1 (without loss of generality, let us suppose that

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then

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. But

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and

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, so

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, yielding

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, contradicting our assumption that all the variables were distinct.

It follows that each of

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,

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, and

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is equal to 1, so we have

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,

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, and

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. Substituting,

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,

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, and

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. Rearrange to get

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,

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, and

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. These equalities quickly yield

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, which again contradicts our assumption that

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are distinct.