• Thumbnail for Exponentiation
    In mathematics, exponentiation, denoted bn, is an operation involving two numbers: the base, b, and the exponent or power, n. When n is a positive integer...
    107 KB (13,693 words) - 20:30, 5 July 2025
  • Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography...
    21 KB (2,759 words) - 02:20, 29 June 2025
  • are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic...
    22 KB (3,382 words) - 02:27, 29 June 2025
  • Thumbnail for Tetration
    tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's up arrow...
    52 KB (6,659 words) - 16:05, 4 July 2025
  • Thumbnail for Cardinal number
    if μ ≤ π. It will be unique (and equal to π) if and only if μ < π. Exponentiation is given by | X | | Y | = | X Y | , {\displaystyle |X|^{|Y|}=\left|X^{Y}\right|...
    26 KB (3,834 words) - 18:49, 17 June 2025
  • Thumbnail for Order of operations
    a property of exponentiation that (ab)c = abc, so it's unnecessary to use serial exponentiation for this. However, when exponentiation is represented...
    48 KB (4,556 words) - 09:46, 9 July 2025
  • mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number...
    7 KB (771 words) - 03:54, 13 May 2025
  • usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing...
    36 KB (4,965 words) - 08:18, 29 March 2025
  • multiplication, hence also exponentiation, of diagonal matrices is equivalent to element-wise addition and multiplication, and hence exponentiation; in particular...
    55 KB (10,481 words) - 17:15, 27 February 2025
  • multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity...
    43 KB (5,798 words) - 13:42, 30 June 2025
  • The use of the caret for exponentiation can be traced back to ALGOL 60,[citation needed] which expressed the exponentiation operator as an upward-pointing...
    11 KB (1,210 words) - 08:56, 1 July 2025
  • Thumbnail for Logarithm
    single-variable function, the logarithm to base b is the inverse of exponentiation with base b. The logarithm base 10 is called the decimal or common logarithm...
    98 KB (11,674 words) - 13:55, 4 July 2025
  • names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function...
    24 KB (3,370 words) - 18:27, 28 May 2025
  • Thumbnail for Diffie–Hellman key exchange
    logarithm problem. The computation of ga mod p is known as modular exponentiation and can be done efficiently even for large numbers. Note that g need...
    47 KB (5,306 words) - 19:04, 2 July 2025
  • Thumbnail for Arithmetic
    subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can...
    165 KB (16,396 words) - 04:14, 2 June 2025
  • Thumbnail for Double exponential function
    A double exponential function is a constant raised to the power of an exponential function. The general formula is f ( x ) = a b x = a ( b x ) {\displaystyle...
    9 KB (1,169 words) - 00:28, 6 February 2025
  • in exponentiation, such as in square and cubic forms, any multiplier prefix is considered part of the unit, and thus included in the exponentiation. 1 km2...
    4 KB (540 words) - 19:24, 18 May 2025
  • Thumbnail for Associative property
    operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties...
    26 KB (3,498 words) - 17:11, 5 July 2025
  • Regardless of the specific algorithm used, this operation is called modular exponentiation. For example, consider Z17×. To compute 3 4 {\displaystyle 3^{4}} in...
    17 KB (2,537 words) - 07:42, 7 July 2025
  • operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices),...
    9 KB (1,133 words) - 21:14, 14 April 2025
  • Thumbnail for Freshman's dream
    freshman's dream is a valid identity. This result demonstrates that exponentiation by p produces an endomorphism, known as the Frobenius endomorphism of...
    9 KB (1,124 words) - 22:24, 4 January 2025
  • in exponentiation, such as in square and cubic forms, any multiples-prefix is considered part of the unit, and thus included in the exponentiation. 1 Mm2...
    4 KB (462 words) - 21:56, 18 April 2025
  • In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions defined...
    3 KB (491 words) - 17:30, 1 June 2025
  • j {\displaystyle U^{2^{j}}} . This can be accomplished via modular exponentiation, which is the slowest part of the algorithm. The gate thus defined satisfies...
    40 KB (5,809 words) - 23:45, 1 July 2025
  • Thumbnail for Fibonacci sequence
    matrix can be computed in O(log n) arithmetic operations, using the exponentiation by squaring method. Taking the determinant of both sides of this equation...
    86 KB (13,080 words) - 14:15, 7 July 2025
  • Thumbnail for Hypercube
    In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is...
    27 KB (2,222 words) - 19:05, 4 July 2025
  • more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units...
    16 KB (387 words) - 14:12, 12 May 2025
  • Thumbnail for Positional notation
    allowed digits for the given base.) Positional numeral systems work using exponentiation of the base. A digit's value is the digit multiplied by the value of...
    52 KB (7,490 words) - 02:41, 4 July 2025
  • Thumbnail for Schanuel's conjecture
    Wilkie, for example, proved that the theory of the real field with exponentiation, R {\displaystyle \mathbb {R} } exp, is decidable provided Schanuel's...
    16 KB (1,935 words) - 22:39, 20 April 2025
  • + 1 contains only small factors. It uses Lucas sequences to perform exponentiation in a quadratic field. It is analogous to Pollard's p − 1 algorithm....
    5 KB (831 words) - 21:06, 30 September 2022