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One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes.”. You check this in your ...
Arithmetic progression. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
is a divergent series. Sequences dn + a with odd d are often ignored because half the numbers are even and the other half is the same numbers as a sequence with 2d, if we start with n = 0. For example, 6n + 1 produces the same primes as 3n + 1, while 6n + 5 produces the same as 3n + 2 except for the only even prime 2. The following table lists ...
The parity sequence is the same as the sequence of operations. Using this form for f(n), it can be shown that the parity sequences for two numbers m and n will agree in the first k terms if and only if m and n are equivalent modulo 2 k. This implies that every number is uniquely identified by its parity sequence, and moreover that if there are ...
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely .[ 1 ] The problem is known to be NP-complete. Moreover, some restricted variants of it are NP-complete too ...
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In number theory, primes in arithmetic progressionare any sequenceof at least three prime numbersthat are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by an=3+4n{\displaystyle a_{n}=3+4n}for 0≤n≤2{\displaystyle 0\leq n\leq 2}. According to the Green–Tao theorem, there ...
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