Search results
Results from the WOW.Com Content Network
A perfect power has a common divisor m > 1 for all multiplicities (it is of the form a m for some a > 1 and m > 1). The first: 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100 (sequence A001597 in the OEIS). 1 is sometimes included. A powerful number (also called squareful) has multiplicity above 1 for all prime
Then, as Lehmer shows, all consecutive pairs of P-smooth numbers are of the form (x i − 1)/2, (x i + 1)/2. Thus one can find all such pairs by testing the numbers of this form for P-smoothness. Lehmer's paper furthermore shows [3] that applying a similar procedure to the equation =,
Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number. For example, 15 is a composite number because 15 = 3 · 5 , but 7 is a prime number because it cannot be decomposed in this way.
When such a divisor is found, the repeated application of this algorithm to the factors q and n / q gives eventually the complete factorization of n. [1] For finding a divisor q of n, if any, it suffices to test all values of q such that 1 < q and q 2 ≤ n. In fact, if r is a divisor of n such that r 2 > n, then q = n / r is a divisor of n ...
Methods that are restricted to specific number forms include Pépin's test for Fermat numbers (1877), [27] Proth's theorem (c. 1878), [28] the Lucas–Lehmer primality test (originated 1856), and the generalized Lucas primality test. [17] Since 1951 all the largest known primes have been found using these tests on computers.
The table below shows all 72 divisors of 10080 by writing it as a product of two numbers in 36 different ways. The highly composite number: 10080 10080 = (2 × 2 × 2 × 2 × 2) × (3 × 3) × 5 × 7
The 28/36 rule says your total housing costs shouldn’t exceed 28% of your gross income, and your total debt shouldn’t exceed 36%. ... multiply that by 0.28 to find the maximum amount you ...
This requires all of its prime factors to be primes of the form 4n + 1. [16] Therefore, c is of the form 4n + 1. A sequence of possible hypotenuse numbers for a primitive Pythagorean triple can be found at (sequence A008846 in the OEIS). The area (K = ab/2) is a congruent number [17] divisible by 6.