1987 USAMO Problems/Problem 3
is the smallest set of polynomials such that:
- 1. belongs to .
- 2. If belongs to , then and both belong to .
Show that if and are distinct elements of , then for any .
Let be an arbitrary polynomial in Then when Define for some and for some
If and we have for all with Therefore for any
For any , Let and for If for then for
Similarly, for any , Let and for If for then for
The proof is done by an induction.
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