Number theory · Digit sums · Congruences · Powers of ten · Diophantine equations · Coprimality
For a positive integer \(x\), let \(S(x)\) denote the sum of the decimal digits of \(x\).
(a) Determine the smallest element of the set \(\{\, S(11n^2 + n + 1) \mid n \text{ a positive integer} \,\}\).
(b) Prove that the smallest value found in (a) is attained for infinitely many positive integers \(n\).
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Serbian National Competition (Drzavno takmicenje) 2026, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source