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Real Roots of Polynomial

Source: 2010 IrMO Paper 2 Problem 2

January 30, 2018
algebrapolynomial

Problem Statement

For each odd integer p≥3p\ge 3 find the number of real roots of the polynomial fp(x)=(x−1)(x−2)⋯(x−p+1)+1.f_p(x)=(x-1)(x-2)\cdots (x-p+1)+1.
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