On the distance between perfect numbers
Philippe Ellia
TL;DR
This paper proves that infinitely many specific triangular numbers cannot be the difference between two perfect numbers, highlighting limitations in the possible gaps between perfect numbers.
Contribution
It establishes the existence of infinitely many triangular numbers, congruent to 3 mod 12, that are not distances between any two perfect numbers.
Findings
Infinitely many triangular numbers are not differences between perfect numbers.
Triangular numbers congruent to 3 mod 12 are excluded as perfect number gaps.
Abstract
It is shown that there exist infinitely many triangular numbers (congruent to 3 mod 12) which cannot be the distance between two perfect numbers.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Mathematics and Applications