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This note explores the distribution of quotients and remainders in multiplication tables, revealing essential arithmetic properties.
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.
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Frédéric D. W. Heidenthal-König (2026) studied this question.
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