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March 4, 2026Euleriana0 citationsOpen Access

Even Repdigits are not Perfect: Conclusions from Triangular Numbers

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UHUwe Hassler

Key Points

  • The aim is to determine if there are nontrivial repdigits that are also perfect numbers, particularly below a large threshold.
  • Analysis of numerical properties of repdigits and perfect numbers
  • Review of existing results related to triangular numbers
  • Discussion of Euler's works on polygonal numbers
  • No nontrivial repdigits exist as perfect numbers for values less than 10^1500
  • Validates previous results in the study of triangular numbers
  • Highlights the significance of Euler's contributions in mathematics

Abstract

Are there nontrivial repdigits that are perfect numbers? This note gives an answer: not for numbers smaller than 10^1500. This finding follows from results for triangular numbers. Passing by, I review Euler's contributions on polygonal numbers.

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Cite This Study

Uwe Hassler (2026) studied this question.

synapsesocial.com/papers/69a7ccc3d48f933b5eed882bhttps://doi.org/10.56031/2693-9908.1098
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