Number theory · Perfect cubes · Diophantine equations · Bounding
Find all natural numbers \(n\) for which the three numbers
\[ n-4, \qquad 2n+2, \qquad 4n+1 \]
are all perfect cubes.
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Serbian Municipal Competition 2019, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source