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June 19, 2026Glasgow Mathematical JournalOpen Access

Small differences between cubic and rational numbers

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Authors

ADArtūras DubickasVilnius University

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Overview

Randomized trial reveals the closeness of cubic and rational numbers, indicating a potential mathematical understanding.

Key Points

  • This paper investigates the proximity of cubic numbers and rational numbers under specific constraints.
  • Proved that for sufficiently large integers, cubic and rational numbers can be closely approximated.
  • Defined a mathematical inequality involving height and explicit construction of the numbers.
  • Demonstrated that the difference between a cubic number and a rational number is less than 272/H^4 for sufficiently large integers.
  • Established that the exponent 4 in the inequality is the best possible under the given conditions.

Cite This Study

Artūras Dubickas (2026) studied this question.

synapsesocial.com/papers/6a34de7065a5b0777af2dd69https://doi.org/10.1017/s0017089526100998
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Also Consider

Synapse has enriched one closely related paper. Consider it for comparative context:

  1. 1Distance Between Cubics and Rationals2026 · 1 citations