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2. Multiplicative inverse - Wikipedia

   en.wikipedia.org/wiki/Multiplicative_inverse

   For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the ...

3. Modular multiplicative inverse - Wikipedia

   en.wikipedia.org/wiki/Modular_multiplicative_inverse

   A modular multiplicative inverse of a modulo m can be found by using the extended Euclidean algorithm. The Euclidean algorithm determines the greatest common divisor (gcd) of two integers, say a and m. If a has a multiplicative inverse modulo m, this gcd must be 1. The last of several equations produced by the algorithm may be solved for this gcd.

4. Formal power series - Wikipedia

   en.wikipedia.org/wiki/Formal_power_series

   Once we have defined multiplication for formal power series, we can define multiplicative inverses as follows. The multiplicative inverse of a formal power series A is a formal power series C such that AC = 1, provided that such a formal power series exists. It turns out that if A has a multiplicative inverse, it is unique, and we denote it by ...

5. Modular exponentiation - Wikipedia

   en.wikipedia.org/wiki/Modular_exponentiation

   For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m).

6. Multiplicative group of integers modulo n - Wikipedia

   en.wikipedia.org/wiki/Multiplicative_group_of...

   Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...

7. Inequality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Inequality_(mathematics)

   The rules for the additive inverse, and the multiplicative inverse for positive numbers, are both examples of applying a monotonically decreasing function. If the inequality is strict ( a < b , a > b ) and the function is strictly monotonic, then the inequality remains strict.

8. Modular arithmetic - Wikipedia

   en.wikipedia.org/wiki/Modular_arithmetic

   The multiplicative inverse x ≡ a −1 (mod m) may be efficiently computed by solving Bézout's equation a x + m y = 1 for x, y, by using the Extended Euclidean algorithm. In particular, if p is a prime number, then a is coprime with p for every a such that 0 < a < p; thus a multiplicative inverse exists for all a that is not congruent to zero ...

9. List of Cyberchase episodes - Wikipedia

   en.wikipedia.org/wiki/List_of_Cyberchase_episodes

   The season premiered with a movie special on April 19, 2019, with the remaining episodes set to begin airing in the fall; [6] However, all but two of the episodes premiered in 2020. [7] A thirteenth season was confirmed by Robert Tinkler, the voice actor of Delete, on X, which premiered on February 25, 2022. [8]