1975 Canadian MO Problems/Problem 8
Let be a positive integer. Find all polynomials where the are real, which satisfy the equation .
|1975 Canadian MO (Problems)|
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Let be the degree of polynomial . We begin by noting that . This is because the degree of the LHS is and the RHS is . Now we split into two cases.
In the first case, is a constant. This means that or if is even.
In the second case, is nonconstant with coefficients of . If we divide by on both sides, then we have that . This can only be achieved if . This is because if we factor out a , then clearly these terms are not constant. Thus, and our second solution is .