Number theory · Integer polynomials · Divisibility of differences · Primes · Parity · Divisor lists · Case analysis
Problem 4, 2010
Let \(P(x)\) be a polynomial with integer coefficients for which there exist prime numbers \(p < q < r\) with
\[ \{P(p),\, P(q),\, P(r)\} = \{20,\, 3,\, 2010\} . \]
Prove that \(P(p+q) = 2010\).
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Serbian National Competition (Drzavno takmicenje) 2010, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source