Algebra · Polynomials · Integer coefficients · Integer roots · Divisibility
Problem 1, 2002
A polynomial \(p(x)\) has integer coefficients. Divided by \(x^2 - 12x + 11\), it leaves the remainder \(990x - 889\). Prove that no integer is a zero of \(p(x)\).
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Serbian Republic Competition (Republicko takmicenje) 2002, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source