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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 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).
A seemingly weaker yet equivalent statement to Bunyakovsky's conjecture is that for every integer polynomial () that satisfies (1)–(3), () is prime for at least one positive integer : but then, since the translated polynomial (+) still satisfies (1)–(3), in view of the weaker statement () is prime for at least one positive integer >, so ...
The Beal conjecture, a generalization of Fermat's Last Theorem proposing that if A, B, C, x, y, and z are positive integers with A x + B y = C z and x, y, z > 2, then A, B, and C have a common prime factor. The abc conjecture would imply that there are only finitely many counterexamples.
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 ...
But in such a large, complex market, items frequently fall through the cracks, so if you do discover a counterfeit item in your Amazon Prime box, Dimyan suggests two actions. "Utilize Amazon's ...
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 ...
We mean it. Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT 'Connections’ hints and answers for #587 on ...