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integer roots f(x) = ax^3 + bx^2 + cx + d

Source: Polish MO second round 1958 p3

August 29, 2024
algebrapolynomial

Problem Statement

Prove that if the polynomial f(x)=ax3+bx2+cx+d f(x) = ax^3 + bx^2 + cx + d with integer coefficients takes odd values for x=0 x = 0 and x=1 x = 1 , then the equation f(x)=0 f(x) = 0 has no integer roots.
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