Search results
Results From The WOW.Com Content Network
If every pair in a set of integers is coprime, then the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger condition than setwise coprimality; every pairwise coprime finite set is also setwise coprime, but the reverse is not true. For example, the ...
If any prime factor were shared by any two of (and hence all three of) d, e, and f then by this last equation that prime would also divide each of a, b, and c. So if a, b, and c are in fact pairwise coprime, then d, e, and f must be pairwise coprime as well. This holds for B and C as well as for A.
It is convenient at this point (per Trautman 1998) to call a triple (a,b,c) standard if c > 0 and either (a,b,c) are relatively prime or (a/2,b/2,c/2) are relatively prime with a/2 odd. If the spinor [m n] T has relatively prime entries, then the associated triple (a,b,c) determined by is a standard triple. It follows that the action of the ...
This definition of disjoint sets can be extended to families of sets and to indexed families of sets. By definition, a collection of sets is called a family of sets (such as the power set, for example). In some sources this is a set of sets, while other sources allow it to be a multiset of sets, with some sets repeated.
In mathematics, Legendre's equation is a Diophantine equation of the form: + + = The equation is named for Adrien-Marie Legendre who proved it in 1785 that it is solvable in integers x, y, z, not all zero, if and only if −bc, −ca and −ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, square-free, pairwise relatively prime integers and also not all ...
The prime is said to "decorate" the letter to which it applies. The same convention is adopted in functional programming, particularly in Haskell. In geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc (and thus latitude, longitude, elevation and right ascension).
If p, q, and r are pairwise relatively prime positive integers then the link of the singularity x p + y q + z r = 0 (in other words, the intersection of a small 3-sphere around 0 with this complex surface) is a Brieskorn manifold that is a homology 3-sphere, called a Brieskorn 3-sphere Σ(p, q, r).
Consequently, a prime number divides at most one prime-exponent Mersenne number. [25] That is, the set of pernicious Mersenne numbers is pairwise coprime. If p and 2p + 1 are both prime (meaning that p is a Sophie Germain prime), and p is congruent to 3 (mod 4), then 2p + 1 divides 2 p − 1. [26]