PreprintCC BY 4.0Zenodo
Self-Referential Decimal Power Towers and Integer Roots: Algebraic Reductions, Combinatorial Variants, and Certified Computational Search
Abstract
This paper investigates generalized self-referential decimal power tower identities of the form \sqrt[k]{T(n)} = n, extending the classic 262144 square-root puzzle to higher root indices k > 2. By leveraging prime valuations and algebraic reductions, we show that non-trivial solutions reduce to power base representations, avoiding intractable tower evaluations. Under strict individual digit constraints, we prove the existence of exact non-trivial solutions with colossal indices exceeding 10^{100} (such as n = 4294967296 and n = 3433683820292512484657849089281) and establish negative search bounds up to 10,000 digits. Full Python search scripts and data verification are included.
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BibTeX
@misc{aleman2026selfreferential,
title = {{Self-Referential Decimal Power Towers and Integer Roots: Algebraic Reductions, Combinatorial Variants, and Certified Computational Search}},
author = {Josue Amaro Aleman},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23463514},
url = {https://zenodo.org/records/23463514},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-Referential Decimal Power Towers and Integer Roots: Algebraic Reductions, Combinatorial Variants, and Certified Computational Search
AU - Josue Amaro Aleman
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23463514
UR - https://zenodo.org/records/23463514
AB - This paper investigates generalized self-referential decimal power tower identities of the form \sqrt[k]{T(n)} = n, extending the classic 262144 square-root puzzle to higher root indices k > 2. By leveraging prime valuations and algebraic reductions, we show that non-trivial solutions reduce to power base representations, avoiding intractable tower evaluations. Under strict individual digit constraints, we prove the existence of exact non-trivial solutions with colossal indices exceeding 10^{100} (such as n = 4294967296 and n = 3433683820292512484657849089281) and establish negative search bounds up to 10,000 digits. Full Python search scripts and data verification are included.
ER -