MathDB

5

Part of 1997 Austrian-Polish Competition

Problems(1)

lQ(p_1)l = lQ(p_2)l = lQ(p_3)l = lQ(p_4 )l = 3, Q(x) = ax^3 + bx^2 + cx + d

Source: Austrian - Polish 1997 APMC

5/3/2020
Let p1,p2,p3,p4p_1,p_2,p_3,p_4 be four distinct primes. Prove that there is no polynomial Q(x)=ax3+bx2+cx+dQ(x) = ax^3 + bx^2 + cx + d with integer coefficients such that ∣Q(p1)∣=∣Q(p2)∣=∣Q(p3)∣=∣Q(p4)∣=3|Q(p_1)| =|Q(p_2)| = |Q(p_3)|= |Q(p_4 )| = 3.
Integer PolynomialprimespolynomialCubic