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sum_{k=5}^{k=49} 11_(k / 2\sqrt[3]{1331_(k} }

Source: Spanish Mathematical Olympiad 1971 P1

December 5, 2022
Sumalgebra

Problem Statement

Calculate ∑k=5k=4911(k21331(k3\sum_{k=5}^{k=49}\frac{11_(k}{2\sqrt[3]{1331_(k}} knowing that the numbers 1111 and 13311331 are written in base k≥4k \ge 4.
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