Algebra · Polynomials · Integer coefficients · Divisibility · Factor theorem
Decide whether there exists a polynomial \(P(x)\) with integer coefficients such that, for some four pairwise distinct integers \(a\), \(b\), \(c\), \(d\),
\[ P(a) = P(b) = P(c) = P(d) = 2024 , \]
and moreover, for some integer \(e\),
(a) \(P(e) = 2028\);
(b) \(P(e) = 2026\).
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Serbian National Competition (Drzavno takmicenje) 2026, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source