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  2. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    One particular solution is x = 0, y = 0, z = 0. Two other solutions are x = 3, y = 6, z = 1, and x = 8, y = 9, z = 2. There is a unique plane in three-dimensional space which passes through the three points with these coordinates, and this plane is the set of all points whose coordinates are solutions of the equation.

  3. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3 , or 3 raised to the 5th power . The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".

  4. Chinese remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Chinese_remainder_theorem

    In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

  5. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    x = Re z is the real part, y = Im z is the imaginary part, r = | z | = √ x 2 + y 2 is the magnitude of z and; φ = arg z = atan2(y, x). φ is the argument of z, i.e., the angle between the x axis and the vector z measured counterclockwise in radians, which is defined up to addition of 2π.

  6. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    Applying the f function k times to the number n = 2 k a + b will give the result 3 c a + d, where d is the result of applying the f function k times to b, and c is how many increases were encountered during that sequence.

  7. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.

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  9. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    For instance, to find the product of 13 and 21 one had to double 21 three times, obtaining 2 × 21 = 42, 4 × 21 = 2 × 42 = 84, 8 × 21 = 2 × 84 = 168. The full product could then be found by adding the appropriate terms found in the doubling sequence: [ 16 ]