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To test the divisibility of a ... Add 7 times the last digit to the rest. ... since 10 × (−3) = −30 = 1 mod 31, we get the rule for using y − 3x in the table ...
Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The naive procedure for verification of the associativity of a binary operation specified by a Cayley table, which compares the two products that can be ...
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
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The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.