Euclidean Decomposition of the Multiplication Table

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