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  2. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    Fermat–Catalan conjecture. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many ...

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

  4. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Tutte's conjectures: every bridgeless graph has a nowhere-zero 5-flow [129] every Petersen - minor -free bridgeless graph has a nowhere-zero 4-flow [130] Woodall's conjecture that the minimum number of edges in a dicut of a directed graph is equal to the maximum number of disjoint dijoins.

  5. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    Interior angle Δθ = θ 1 −θ 2. The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines, which states that where is the angle between sides and . [45] When is radians or 90°, then , and the formula reduces to the usual Pythagorean theorem.

  6. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.

  7. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    v. t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has where e is the base of the natural logarithm, i is the imaginary ...

  8. Double exponential function - Wikipedia

    en.wikipedia.org/wiki/Double_exponential_function

    A double exponential function (red curve) compared to a single exponential function (blue curve). A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a>1 and b>1), which grows much more quickly than an exponential function. For example, if a = b = 10: f (x) = 10 10x. f (0) = 10.

  9. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = ⁡ or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

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