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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 ...
The essential idea behind trial division tests to see if an integer n, the integer to be factored, can be divided by each number in turn that is less than the square root of n. For example, to find the prime factors of n = 70 , one can try to divide 70 by successive primes: first, 70 / 2 = 35 ; next, neither 2 nor 3 evenly divides 35 ; finally ...
The Solovay–Strassen test is an Euler probable prime test (see PSW [3] page 1003). For each individual value of a, the Solovay–Strassen test is weaker than the Miller–Rabin test. For example, if n = 1905 and a = 2, then the Miller-Rabin test shows that n is composite, but the Solovay–Strassen test does not.
Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations. Digit sums ...
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.
Sanity tests may sometimes be used interchangeably with smoke tests [3] insofar as both terms denote tests which determine whether it is possible and reasonable to continue testing further. On the other hand, a distinction is sometimes made that a smoke test is a non-exhaustive test that ascertains whether the most crucial functions of a ...
Fermat's little theorem is the basis for the Fermat primality test and is one of the fundamental results of elementary number theory. The theorem is named after Pierre de Fermat, who stated it in 1640. It is called the "little theorem" to distinguish it from Fermat's Last Theorem. [3]
The above formula can be used as a primality test in the sense that ... The divisibility of Fibonacci numbers by a prime p is related to the ... Example 3. p = 13, ...