Explores expressing three consecutive integers as sums of three cubes, suggesting possibilities for further exploration.
This paper is concerned with the problem of expressing three consecutive integers as sums of three cubes. We give several parametric solutions of the problem. We also give some examples of five and seven consecutive integers that can all be expressed as sums of three cubes. We conclude the paper with an open problem regarding four or more consecutive integers expressible as sums of three cubes.
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Ajai Choudhry (2026) studied this question.
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