January by a well-ordered index set. Since, for a given element g of
... The crossing number problem for the complete bipartite graph, K,",", on m + n vertices, whose mn edges are just those which join one of the m vertices to one of the n, first appeared as Turin's brick-factory problem . For some years it was thought that Zarankiewicz [22] and Urbaník [21] had solved t ...
... The crossing number problem for the complete bipartite graph, K,",", on m + n vertices, whose mn edges are just those which join one of the m vertices to one of the n, first appeared as Turin's brick-factory problem . For some years it was thought that Zarankiewicz [22] and Urbaník [21] had solved t ...
sets
... (n mod 7 = 5), (n mod 11 = 7), (n mod 17 = 9) Knowing the language “Math” can help us look for information and use various systems to solve this problem. The following exolains how to use SAGE's set operations to solve problems. ...
... (n mod 7 = 5), (n mod 11 = 7), (n mod 17 = 9) Knowing the language “Math” can help us look for information and use various systems to solve this problem. The following exolains how to use SAGE's set operations to solve problems. ...
H6
... 2. In this problem we want to try and understand the “sums of two squares” problem for polynomials over R. The question is: When can a polynomial n(x) ∈ R[x] be written as the sum of two squares, n(x) = (f (x))2 + (g(x))2 , with f (x), g(x) ∈ R[x]? We will use one fact not proved in this class: Eve ...
... 2. In this problem we want to try and understand the “sums of two squares” problem for polynomials over R. The question is: When can a polynomial n(x) ∈ R[x] be written as the sum of two squares, n(x) = (f (x))2 + (g(x))2 , with f (x), g(x) ∈ R[x]? We will use one fact not proved in this class: Eve ...
A characterization of all equilateral triangles in Z³
... at least three prime factors and numerical evidence suggests that the following conjecture is true: Conjecture: The Diophantine equation (4) has degenerate solutions if and only if d has at least three distinct prime factors of the form 4k + 1, k ∈ N. One can easily prove the necessity part of this ...
... at least three prime factors and numerical evidence suggests that the following conjecture is true: Conjecture: The Diophantine equation (4) has degenerate solutions if and only if d has at least three distinct prime factors of the form 4k + 1, k ∈ N. One can easily prove the necessity part of this ...
LP.092314
... The integers is a subset of the real numbers…they are also called signed numbers or simply negative and positive numbers. The set of integers is an infinite set {…-4, -3, -2, -1, 0, 1, 2, 3, 4…} ...
... The integers is a subset of the real numbers…they are also called signed numbers or simply negative and positive numbers. The set of integers is an infinite set {…-4, -3, -2, -1, 0, 1, 2, 3, 4…} ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.