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...

Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography...

are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic...

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...

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|...

a property of exponentiation that (ab)c = abc, so it's unnecessary to use serial exponentiation for this. However, when exponentiation is represented...

mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number...

multiplication, hence also exponentiation, of diagonal matrices is equivalent to element-wise addition and multiplication, and hence exponentiation; in particular...

usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing...

multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity...

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...

names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function...

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...

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...

subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can...

operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties...

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...

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...

Regardless of the specific algorithm used, this operation is called modular exponentiation. For example, consider Z17×. To compute 3 4 {\displaystyle 3^{4}} in...

freshman's dream is a valid identity. This result demonstrates that exponentiation by p produces an endomorphism, known as the Frobenius endomorphism of...

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...

operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices),...

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...

more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units...

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...

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...

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...

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...

Wilkie, for example, proved that the theory of the real field with exponentiation, R {\displaystyle \mathbb {R} } exp, is decidable provided Schanuel's...

+ 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....