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VMO 1995 — Division A Question 5

VMO · VMO 1995 — Division A

Question 5

Determine all polynomials $p(x)$ such that, for every $a\gt 1995$, the equation $p(x)=a$ has more than $1995$ real roots, all greater than $1995$ (a root of multiplicity greater than one is counted according to that multiplicity).