Vol. 9 No. 2 (2025): Vol 9, Iss 2, Year 2025
Articles

Relation Between Class Number and Existence of Perfect Numbers

Dhakshinamurthy S
Department of Mathematics, Sacred Heart College, Tirupattur, Tirupattur District, Tamil Nadu, South India.
Britto Antony Xavier
Department of Mathematics, Sacred Heart College, Tirupattur, Tirupattur District, Tamil Nadu, South India.
Published December 20, 2025
Keywords
  • Perfect numbers, Class numbers, Mersenne primes, Divisor sum formula, Even perfect numbers, Odd perfect numbers, Number theory, Prime distribution.
How to Cite
Dhakshinamurthy S, & Britto Antony Xavier. (2025). Relation Between Class Number and Existence of Perfect Numbers. Journal of Computational Mathematica, 9(2), 105-119. https://doi.org/10.26524/cm222

Abstract

This work explores the relation between class numbers and perfect numbers through divisor sum formulas. It provides a structured derivation showing that even perfect numbers take the form N = 2m(2m+1 1) where (2m+1 1)is prime. The converse is also established, illustrating that such numbers are necessarily perfect. The study employs fundamental number-theoretic principles and factorization techniques to support the results

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