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A family of subsets of is called ultra if and any of the following equivalent conditions are satisfied: [2] [3] For every set S ⊆ X {\displaystyle S\subseteq X} there exists some set B ∈ U {\displaystyle B\in U} such that B ⊆ S {\displaystyle B\subseteq S} or B ⊆ X ∖ S {\displaystyle B\subseteq X\setminus S} (or equivalently, such ...
Maxima (voiced by Amy Johnston) - A comrade of Windblade. She is killed by Menasor. She is killed by Menasor. Victorion (voiced by Anna Akana (Combiner Wars), Kari Wahlgren (Titans Return, Power of the Primes)) - Victorion is the combined robot form of the six Torchbearers - Pyra Magna , Stormclash , Skyburst , Dust Up , Jumpstream , and Rust ...
q-3, q-4, q-9, q-12 are quadratic nonresidues q-3, q-4, q-9, and, for q > 11, q-12 are primitive roots; If p is a Sophie Germain prime greater than 3, then p must be congruent to 2 mod 3. For, if not, it would be congruent to 1 mod 3 and 2p + 1 would be congruent to 3 mod 3, impossible for a prime number. [16]
The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that π c,a (x) and π c,b (x) change places when a and b are coprime to c. [34] Granville and Martin give a thorough exposition and survey. [33] Graph of the number of primes ending in 1, 3, 7, and 9 up to n ...
The first thousand values of φ(n).The points on the top line represent φ(p) when p is a prime number, which is p − 1. [1]In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n.
A megaprime is a prime number with at least one million decimal digits. [1]Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits [2] (of which the smallest is 10 999 +7), [3] and "gigantic prime" for a prime with at least 10,000 digits [4] (of which the smallest is 10 9999 +33603).
Sub.3.3.1 Another condition in which the min-max and max-min are equal is when the Lagrangian has a saddle point : (x∗, λ∗) is a saddle point of the Lagrange function L if and only if x∗ is an optimal solution to the primal, λ∗ is an optimal solution to the dual, and the optimal values in the indicated problems are equal to each other ...
Remington Ultra Magnum, or RUM, refers to a "family" of cartridges developed between 1999 and 2002 by Remington Arms. [1] All of the RUM cartridges are based on the .404 Jeffery non-belted magnum cartridge.