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(i) By Wilson's Theorem:
But note that and so on...
Now if then
(iii) This shows that you have at least 2 solutions if ( a²=(-a)² )
(Let be odd).
Define as .
This polynomial has degree . But every solves this polynomial.
Thus, has value of zero for distinct values, and so it must be a zero polynomial.
So let and we get:
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