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In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
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The polynomial 3x 2 − 5x + 4 is written in descending powers of x. The first term has coefficient 3, indeterminate x, and exponent 2. In the second term, the coefficient is −5. The third term is a constant. Because the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two.
In mathematics, the greatest common divisor(GCD) of two or more integers, which are not all zero, is the largest positive integer that divideseach of the integers. For two integers x, y, the greatest common divisor of xand yis denoted gcd(x,y){\displaystyle \gcd(x,y)}. For example, the GCD of 8 and 12 is 4, that is, gcd(8, 12) = 4.
The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially. That is, for each , there is some with . If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1.
Perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
Even for the first root that involves at most two square roots, the expression of the solutions in terms of radicals is usually highly complicated. However, when no square root is needed, the form of the first solution may be rather simple, as for the equation x 5 − 5x 4 + 30x 3 − 50x 2 + 55x − 21 = 0, for which the only real solution is
"3" is the seventh episode of the second season of the American science fiction television series The X-Files. First broadcast on the Fox network on November 4, 1994 , the episode was written by Glen Morgan , James Wong and Chris Ruppenthal , directed by David Nutter , and featured guest appearances by Perrey Reeves and Malcolm Stewart .