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  2. Cyclotomic field - Wikipedia

    en.wikipedia.org/wiki/Cyclotomic_field

    In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to , the field of rational numbers. [1]Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem.

  3. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    In the base ten number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 10 3 = 1000 and 10 −4 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers.

  4. Proof of Fermat's Last Theorem for specific exponents

    en.wikipedia.org/wiki/Proof_of_Fermat's_Last...

    Since u = 2m 2 = 2de, and since d and e are coprime, they must be squares themselves, d = g 2 and e = h 2. This gives the equation v = d 2 − e 2 = g 4 − h 4 = k 2. The solution (g, h, k) is another solution to the original equation, but smaller (0 < g < d < x). Applying the same procedure to (g, h, k) would produce another solution, still ...

  5. Solenoid valve - Wikipedia

    en.wikipedia.org/wiki/Solenoid_valve

    Ordinary valves can have many ports and fluid paths. A 2-way valve, for example, has 2 ports; if the valve is open, then the two ports are connected and fluid may flow between the ports; if the valve is closed, then ports are isolated. If the valve is open when the solenoid is not energized, then the valve is termed normally open (N.O.).

  6. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.

  7. Degree of a field extension - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_field_extension

    The complex numbers are a field extension over the real numbers with degree [C:R] = 2, and thus there are no non-trivial fields between them. The field extension Q(√ 2, √ 3), obtained by adjoining √ 2 and √ 3 to the field Q of rational numbers, has degree 4, that is, [Q(√ 2, √ 3):Q] = 4.

  8. American Airlines loses US appeal of ruling barring JetBlue ...

    www.aol.com/news/american-airlines-loses-us...

    Siding with the U.S. Department of Justice, the Boston-based 1st U.S. Circuit Court of Appeals affirmed a trial judge's ruling blocking the airlines' "Northeast Alliance," which had allowed the ...

  9. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...

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