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Solving these two quintics yields r = 1.501 × 10 9 m for L 2 and r = 1.491 × 10 9 m for L 1. The Sun–Earth Lagrangian points L 2 and L 1 are usually given as 1.5 million km from Earth. If the mass of the smaller object ( M E ) is much smaller than the mass of the larger object ( M S ), then the quintic equation can be greatly reduced and L ...
(In fact, if n is neither 1 nor 2, then k is either 0 or 1. Besides, if n is not a power of 2, then k is always equal to 0) g is 1 or the largest odd prime factor of n. h is odd, coprime with n, and its prime factors are exactly the odd primes p such that n is the multiplicative order of b modulo p.
The Hoffman–Singleton theorem states that any Moore graph with girth 5 must have degree 2, 3, 7, or 57. The Moore graphs are: [3] The complete graphs K n on n > 2 nodes (diameter 1, girth 3, degree n − 1, order n) The odd cycles C 2n+1 (diameter n, girth 2n + 1, degree 2, order 2n + 1). This includes C 5 with diameter 2, girth 5, degree 2 ...
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2 −1) is a right arithmetic shift, a (0) results in no operation (since 2 0 = 1 is the multiplicative identity element), and a (2 1) results in a left arithmetic shift ...
The following names are assigned to polynomials according to their degree: [2] [3] [4] Special case – zero (see § Degree of the zero polynomial, below) Degree 0 – non-zero constant [5] Degree 1 – linear; Degree 2 – quadratic; Degree 3 – cubic; Degree 4 – quartic (or, if all terms have even degree, biquadratic) Degree 5 – quintic
Abel–Ruffini theorem refers also to the slightly stronger result that there are equations of degree five and higher that cannot be solved by radicals. This does not follow from Abel's statement of the theorem, but is a corollary of his proof, as his proof is based on the fact that some polynomials in the coefficients of the equation are not ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The fundamental theorem of algebra states that every polynomial of positive degree has at least one complex root. The above process shows the fundamental theorem of algebra implies that every polynomial p(x) = a n x n + a n−1 x n−1 + ⋯ + a 1 x + a 0 can be factored as = (),