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Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ 1 (mod n). It exists precisely when a is coprime to n, because in that case gcd(a, n) = 1 and by Bézout's lemma there are integers x and y satisfying ax + ny = 1.
Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: 1 − x 2 1 + x 2 {\displaystyle {\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials , for which algebraic expressions may be solutions .
As of 20 August 2020, a video containing the song, misspelt as "Johny" and uploaded to YouTube by Loo Loo Kids in 2016, [1] has more than 6.9 billion views as of January 2024, making it the third-most-viewed video on the site, as well as the most-viewed nursery rhyme video and one of the top 10 most-disliked YouTube videos.
a 1 a 2 ≡ b 1 b 2 (mod m) (compatibility with multiplication) a k ≡ b k (mod m) for any non-negative integer k (compatibility with exponentiation) p(a) ≡ p(b) (mod m), for any polynomial p(x) with integer coefficients (compatibility with polynomial evaluation) If a ≡ b (mod m), then it is generally false that k a ≡ k b (mod m ...
If p is a prime number which is not a divisor of b, then ab p−1 mod p = a mod p, due to Fermat's little theorem. Inverse: [(−a mod n) + (a mod n)] mod n = 0. b −1 mod n denotes the modular multiplicative inverse, which is defined if and only if b and n are relatively prime, which is the case when the left hand side is defined: [(b −1 ...
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.
The solutions –1 and 2 of the polynomial equation x 2 – x + 2 = 0 are the points where the graph of the quadratic function y = x 2 – x + 2 cuts the x-axis. In general, an algebraic equation or polynomial equation is an equation of the form =, or = [a]
The Indonesian Wikipedia (Indonesian: Wikipedia bahasa Indonesia, WBI for short) is the Indonesian language edition of Wikipedia. It is the fifth-fastest-growing Asian-language Wikipedia after the Japanese, Chinese, Korean, and Turkish language Wikipedias. It ranks 25th in terms of depth among Wikipedias.