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|Q(p_1)| = |Q(p_2)| = |Q(p_3)| = 11 , integer trinomials

Source: Switzerland - Swiss TST 2003 p7

February 18, 2020
trinomialpolynomialquadratic polynomialalgebra

Problem Statement

Find all polynomials Q(x)=ax2+bx+cQ(x)= ax^2+bx+c with integer coefficients for which there exist three different prime numbers p1,p2,p3p_1, p_2, p_3 such that ∣Q(p1)∣=∣Q(p2)∣=∣Q(p3)∣=11|Q(p_1)| = |Q(p_2)| = |Q(p_3)| = 11.
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