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In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form (p, p + 2, p + 6) or (p, p + 4, p + 6). [1]
For example, the numbers 5 and 11 are both sexy primes, because both are prime and =. The term "sexy prime" is a pun stemming from the Latin word for six: sex . If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime triplet .
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).
[6]: p.7 For example, parent (3, 4, 5) has excircle radii equal to 2, 3 and 6. These are precisely the inradii of the three children (5, 12, 13), (15, 8, 17) and (21, 20, 29) respectively. If either of A or C is applied repeatedly from any Pythagorean triple used as an initial condition, then the dynamics of any of a , b , and c can be ...
Wade and Wade [17] first introduced the categorization of Pythagorean triples by their height, defined as c − b, linking 3,4,5 to 5,12,13 and 7,24,25 and so on. McCullough and Wade [18] extended this approach, which produces all Pythagorean triples when k > h √ 2 /d: Write a positive integer h as pq 2 with p square-free and q positive.
The goal is to construct m triplets, each of which contains one element from A, one from B and one from C, such that the sum of each triplet is T. [ 2 ] The 4-partition problem is a variant in which S contains n = 4 m integers, the sum of all integers is m T {\displaystyle mT} , and the goal is to partition it into m quadruplets, all ...
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