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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′ (mod m) holds true. The algorithm ends when the loop has been executed e times.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
In fact, x ≡ b m n −1 m + a n m −1 n (mod mn) where m n −1 is the inverse of m modulo n and n m −1 is the inverse of n modulo m. Lagrange's theorem : If p is prime and f ( x ) = a 0 x d + ... + a d is a polynomial with integer coefficients such that p is not a divisor of a 0 , then the congruence f ( x ) ≡ 0 (mod p ) has at most d ...
The initial formula language was created by a Microsoft team led by Vijay Mital, Robin Abraham, Shon Katzenberger and Darryl Rubin as part of the Tangram and Siena projects. [ 8 ] [ 7 ] Later, as part of Power Apps, Greg Lindhorst and Mike Stall led the effort to enhance the language to what is now become Power Fx.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
Use the extended Euclidean algorithm to compute k −1, the modular multiplicative inverse of k mod 2 w, where w is the number of bits in a word. This inverse will exist since the numbers are odd and the modulus has no odd factors. For each number in the list, multiply it by k −1 and take the least significant word of the result.
The AlphaTauri AT02 is a Formula One racing car designed and constructed by Scuderia AlphaTauri to compete in the 2021 Formula 1 World Championship. The car was driven by Yuki Tsunoda and Pierre Gasly. [2] The AT02 is the second car to be built and run under the AlphaTauri name.
A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.