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Lucas-Lehmer criterion for primality of Mersenne numbers
Lucas-Lehmer criterion for primality of Mersenne numbers

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... 9.2.5: Simplify other roots. • To simplify cube roots, look for factors that are perfect cubes. A perfect cube is a number with a rational cube root. • For example, 3 64  4 , and because 4 is a rational number, 64 is a perfect cube. • For all real number for which the indicated roots exist, ...
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System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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