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month (full) mo ≡ 30 d [23] = 2.592 × 10 6 s [note 3] month (Greg. av.) mo = 30.436 875 d: ≈ 2.6297 Ms [note 3] month (hollow) mo ≡ 29 d [23] = 2.5056 Ms [note 3] Month : mo Cycle time of moon phases ≈ 29.530 589 d (average) ≈ 2.551 Ms: octaeteris = 48 mo (full) + 48 mo (hollow) + 3 mo (full) [24] [25] = 8 a of 365.25 d = 2922 d ...
If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:
If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization ; the result is always unique up to the order of the factors by the prime factorization theorem .
The formula is as follows: [18] [19] A main effect for a factor with s levels has s−1 degrees of freedom. The interaction of two factors with s 1 and s 2 levels, respectively, has (s 1 −1)(s 2 −1) degrees of freedom. The formula for more than two factors follows this pattern.
where both factors have integer coefficients (the fact that Q has integer coefficients results from the above formula for the quotient of P(x) by /). Comparing the coefficients of degree n and the constant coefficients in the above equality shows that, if p q {\displaystyle {\tfrac {p}{q}}} is a rational root in reduced form , then q is a ...
The great disadvantage of Euler's factorization method is that it cannot be applied to factoring an integer with any prime factor of the form 4k + 3 occurring to an odd power in its prime factorization, as such a number can never be the sum of two squares.
Fractional designs are expressed using the notation l k − p, where l is the number of levels of each factor, k is the number of factors, and p describes the size of the fraction of the full factorial used. Formally, p is the number of generators; relationships that determine the intentionally confounded effects that reduce the number of runs ...
Squares are always congruent to 0, 1, 4, 5, 9, 16 modulo 20. The values repeat with each increase of a by 10. In this example, N is 17 mod 20, so subtracting 17 mod 20 (or adding 3), produces 3, 4, 7, 8, 12, and 19 modulo 20 for these values. It is apparent that only the 4 from this list can be a square.