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