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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 ...
There are infinitely many different Lissajous knots, [4] and other examples with 10 or fewer crossings include the 7 4 knot, the 8 15 knot, the 10 1 knot, the 10 35 knot, the 10 58 knot, and the composite knot 5 2 * # 5 2, [1] as well as the 9 16 knot, 10 76 knot, the 10 99 knot, the 10 122 knot, the 10 144 knot, the granny knot, and the composite knot 5 2 # 5 2. [5]
The first step is relatively slow but only needs to be done once. Modular multiplicative inverses are used to obtain a solution of a system of linear congruences that is guaranteed by the Chinese Remainder Theorem. For example, the system X ≡ 4 (mod 5) X ≡ 4 (mod 7) X ≡ 6 (mod 11) has common solutions since 5,7 and 11 are pairwise coprime ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. The term is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping.
Pairwise compatibility graphs were first introduced by Paul Kearney, J. Ian Munro and Derek Phillips in the context of phylogeny reconstruction. When sampling from a phylogenetic tree, the task of finding nodes whose path distance lies between given lengths d m i n < d m a x {\displaystyle d_{min}<d_{max}} is equivalent to finding a clique in ...
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
As a result, for every set of relatively prime numbers {, …,} there exists a value of such that every larger number is representable as a linear combination of {, …,} in at least one way. This consequence of the theorem can be recast in a familiar context considering the problem of changing an amount using a set of coins.