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To test for divisibility by D, where D ends in 1, 3, 7, or 9, the following method can be used. [12] Find any multiple of D ending in 9. (If D ends respectively in 1, 3, 7, or 9, then multiply by 9, 3, 7, or 1.) Then add 1 and divide by 10, denoting the result as m. Then a number N = 10t + q is divisible by D if and only if mq + t is divisible ...
Dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions. A person who has calculated the power output of a car to be 700 kJ may have omitted a factor, since the unit joules is a measure of energy, not power (energy per unit time).
The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. [1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [2]
These tests typically require factorization of n + 1, n − 1, or a similar quantity, which means that they are not useful for general-purpose primality testing, but they are often quite powerful when the tested number n is known to have a special form. The Lucas test relies on the fact that the multiplicative order of a number a modulo n is n ...
If we order the integers in the interval [1, 2n] by divisibility, the subinterval [n + 1, 2n] forms an antichain with cardinality n. A partition of this partial order into n chains is easy to achieve: for each odd integer m in [1,2 n ], form a chain of the numbers of the form m 2 i .
PDF is a standard for encoding documents in an "as printed" form that is portable between systems. However, the suitability of a PDF file for archival preservation depends on options chosen when the PDF is created: most notably, whether to embed the necessary fonts for rendering the document; whether to use encryption; and whether to preserve additional information from the original document ...
6: an even number that passes the divisibility test for 3. 7: sum of all the digits is a multiple of 7. 5: successive subtraction of final two digits from all the other digits yields a multiple of 5. 12: an even number that passes the divisibility test for 5. Base 11 (a prime base, for comparison): 2: sum of all the digits is a multiple of 2.
The non-negative integers partially ordered by divisibility. The division lattice is an infinite complete bounded distributive lattice whose elements are the natural numbers ordered by divisibility. Its least element is 1, which divides all natural numbers, while its greatest element is 0, which is divisible by all natural numbers.