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The modular square root of can be taken this way. Having solved the associated quadratic equation we now have the variables w and set v = r (if C in the quadratic is a natural square). Solve for variables α {\displaystyle \alpha } and β {\displaystyle \beta } the following equation:
Hensel's original lemma concerns the relation between polynomial factorization over the integers and over the integers modulo a prime number p and its powers. It can be straightforwardly extended to the case where the integers are replaced by any commutative ring, and p is replaced by any maximal ideal (indeed, the maximal ideals of have the form , where p is a prime number).
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r 2 ≡ n (mod p), where p is a prime: that is, to find a square root of n modulo p.
Yalda Night, or Shab-e Yalda (also spelled Shabe Yalda), marks the longest night of the year in Iran and in many other Central Asian and Middle Eastern countries. On the winter solstice, in a ...
If x is a simple root of the polynomial , then Laguerre's method converges cubically whenever the initial guess, , is close enough to the root . On the other hand, when x 1 {\displaystyle \ x_{1}\ } is a multiple root convergence is merely linear, with the penalty of calculating values for the polynomial and its first and second derivatives at ...
Dylan Andrews banked in a 3-pointer with 0.4 seconds remaining to give UCLA a 73-71 victory over No. 12 Oregon on Sunday, the Ducks' first loss of the season. Eric Dailey Jr. had 19 points to lead ...
High school football enthusiasts who want to place a bet on a big game have no choice but to turn to an offshore site. Accepting a wager on high school sports is outlawed in Nevada and other U.S ...
In number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the equation (or congruence) (). If k is the smallest such exponent for x , then x is called a primitive k th root of unity modulo n . [ 1 ]