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This is a Quantitative Study study.

October 8, 2025Open Access

A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers

Key Points

The analysis shows a defined polynomial related to higher-order generalized Lehmer-Euler numbers.
It finds that the q-supercongruence has significant implications in the study of related number theory concepts.
New definitions include polynomials that expand on previous Euler number generalizations.
The mathematical exploration relies on the historical context of Lehmer's 1935 definitions.

Abstract

Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, we define a new polynomial related to the higher-order generalized Lehmer-Euler numbers and determine its a q-supercongruence.

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Cite This Study

Weiwei Qi (Sat,) studied this question.

synapsesocial.com/papers/68e6494525bc5bdb9871397a https://doi.org/https://doi.org/10.48550/arxiv.2507.16825

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