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In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
Solving for , = = = = = Thus, the power rule applies for rational exponents of the form /, where is a nonzero natural number. This can be generalized to rational exponents of the form p / q {\displaystyle p/q} by applying the power rule for integer exponents using the chain rule, as shown in the next step.
In mathematics, an algebraic expression is an expression build up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Inputs An integer b (base), integer e (exponent), and a positive integer m (modulus) Outputs The modular exponent c where c = b e mod m. Initialise c = 1 and loop variable e′ = 0; While e′ < e do Increment e′ by 1; Calculate c = (b ⋅ c) mod m; Output c; Note that at the end of every iteration through the loop, the equation c ≡ b e ...
"Galois representations and modular forms" (PDF). Discusses various material which is related to the proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey's construction, and the conjectures of Serre and of Taniyama–Shimura. Shay, David (2003). "Fermat's Last Theorem".
The text-only form of the LaTeX can be set via user preferences at My Preferences – Appearance – Math. The hidden MathML can be used by screen readers and other assistive technology. To display the MathML in Firefox: Install the Native MathML extension; Or copy its CSS rules to your Wikipedia user stylesheet.
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In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]
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