problem 1 of Indian Mathematical Olympiad 1989
Source: poynomial factorization
September 1, 2009
algebrapolynomialcalculusintegrationquadraticsmodular arithmeticalgebra unsolved
Problem Statement
Prove that the Polynomial f(x) \equal{} x^{4} \plus{} 26x^{3} \plus{} 56x^{2} \plus{} 78x \plus{} 1989 can't be expressed as a product f(x) \equal{} p(x)q(x) , where and are both polynomial with integral coefficients and with degree at least .