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To test the divisibility of a number by a power of 2 or a power of 5 (2 n or 5 n, in which n is a positive integer), one only need to look at the last n digits of that number. To test divisibility by any number expressed as the product of prime factors p 1 n p 2 m p 3 q {\displaystyle p_{1}^{n}p_{2}^{m}p_{3}^{q}} , we can separately test for ...
Since 2 divides , +, and +, and 3 divides and +, the only possible remainders mod 6 for a prime greater than 3 are 1 and 5. So, a more efficient primality test for is to test whether is divisible by 2 or 3, then to check through all numbers of the form + and + which are .
Additionally, since the smallest four primes (2, 3, 5, 7) are either divisors or neighbors of 6, senary has simple divisibility tests for many numbers. Furthermore, all even perfect numbers besides 6 have 44 as the final two digits when expressed in senary, which is proven by the fact that every even perfect number is of the form 2 p – 1 (2 p ...
For example, if a = 2 and p = 7, then 2 6 = 64, and 64 − 1 = 63 = 7 × 9 is a multiple of 7. 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.
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.
6. Spare Keys. Spare keys in your wallet might seem like a good idea — until you lose them. Now, some random guy could be two steps away from showing himself in. Better call: leave a spare with ...
3. Keebler Fudge Magic Middles. Neither the chocolate fudge cream inside a shortbread cookie nor versions with peanut butter or chocolate chip crusts survived.
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).