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m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
For n ≥ 2, a(n) is the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached; a(n) = −1 if no prime is ever reached. A037274
This article gives a list of conversion factors for several physical quantities. ... = 50.802 345 44 kg: hundredweight (short); ... ≈ 70.337 057 W:
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
Indeed, in this proposition the exponents are all equal to one, so nothing is said for the general case. While Euclid took the first step on the way to the existence of prime factorization, Kamāl al-Dīn al-Fārisī took the final step [ 8 ] and stated for the first time the fundamental theorem of arithmetic.
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. [1] [2] For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 7 2 and 15750 = 2 × 3 2 × 5 3 × 7 are both 7-smooth, while 11 and 702 = 2 × 3 3 × 13 are not 7-smooth.
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 ...
The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. [1]
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