PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
March 13, 20260 citationsOpen Access

Euclidean Decomposition of the Multiplication Table

View Full Paper
FHFrédéric D. W. Heidenthal-König

Key Points

  • The aim is to analyze the joint distribution of quotients and remainders from Euclidean division of multiplication table entries.
  • Introduction of the array A(n,q,r) to record distributions
  • Analysis of the n×n multiplication table entries
  • Projection of classical arithmetic quantities from A(n,q,r)
  • Identification of quotient and remainder distributions
  • Presentation of divisor counts as a function of the array
  • Recognition of distinct products in the multiplication table as projections of the array

Abstract

This note introduces the array A(n,q,r) that records the joint distribution of quotient and remainder obtained by applying Euclidean division to entries of the n×n multiplication table. Several classical arithmetic quantities appear as projections of this array, including quotient and remainder distributions, divisor counts, multiplicative support, and the set of distinct products occurring in the multiplication table.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Frédéric D. W. Heidenthal-König (2026) studied this question.

synapsesocial.com/papers/69b3ab9102a1e69014ccc816https://doi.org/10.5281/zenodo.18960358
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Divisor–Window Formula for the Euclidean Decomposition of the Multiplication Table2026
  2. 2Euclidean Transport of Multiplication2026
  3. 3Euclidean Decomposition of the Multiplication Table: Papers and Parallels2026
  4. 4Projective Geometry of the Divisor Lattice: Reconstructing Arithmetic from Quasimodular Residues2026
  5. 5The A-C Coupling Theorem: Extension from Three to Four Variables2026