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Fermat's little theorem states that if p is prime and a is coprime to p, then a p−1 − 1 is divisible by p.For an integer a > 1, if a composite integer x divides a x−1 − 1, then x is called a Fermat pseudoprime to base a.
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
A user will input a number and the Calculator will use an algorithm to search for and calculate closed-form expressions or suitable functions that have roots near this number. Hence, the calculator is of great importance for those working in numerical areas of experimental mathematics. The ISC contains 54 million mathematical constants.
DIN 41612-6: Two-part connection for printed boards; grid 2.54mm; dimensions of types Q, R and S: Withdrawn: DIN EN 60603-2: EN 60603-2: DIN 41612-7: Two-part connectors for printed boards; grid 2,54 mm; dimensions of types U and V: Withdrawn: DIN EN 60603-2: EN 60603-2: DIN 41612-8: Two-part connectors for printed boards; grid 2.54 mm ...
Unlike the list above, that page excludes the bases 1 and n−1. When p is a prime, p 2 is a Fermat pseudoprime to base b if and only if p is a Wieferich prime to base b. For example, 1093 2 = 1194649 is a Fermat pseudoprime to base 2, and 11 2 = 121 is a Fermat pseudoprime to base 3.
In fact, 341 is the smallest pseudoprime base 2 (see Figure 1 of [3]). There are only 21853 pseudoprimes base 2 that are less than 2.5 × 10 10 (see page 1005 of [ 3 ] ). This means that, for n up to 2.5 × 10 10 , if 2 n −1 (modulo n ) equals 1, then n is prime, unless n is one of these 21853 pseudoprimes.
In computer science, pseudopolynomial time number partitioning is a pseudopolynomial time algorithm for solving the partition problem. The problem can be solved using dynamic programming when the size of the set and the size of the sum of the integers in the set are not too big to render the storage requirements infeasible.
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.