Randomized trial investigates Kucius Conjecture in integers, suggesting it holds for all n ≥ 5.
Problems on sums of equal powers are classic research topics in elementary number theory. Kucius Conjecture is a newly proposed problem in this research field. This paper adopts complete inequality estimation, integer constraint analysis, binomial expansion and monotonic function proof to give a fully self-contained, rigorous proof with all auxiliary lemmas and numerical verifications attached. The final result proves the conjecture holds for all integers n ≥ 5.
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Mingguang Liu (2026) studied this question.
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