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This equation is basically Pell's equation or the negative Pell equation and its solutions can be obtained similarly using the continued fraction expansion of . Whether or not x 2 − Δ y 2 = −4 has a solution determines whether or not the class group of K is the same as its narrow class group , or equivalently, whether or not there is a ...
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools. [1] [2]
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. [1]
In 1962, Biggs gained first-class honours in his third year of the university's undergraduate degree in mathematics. [2] 1946–1952: Uxendon Manor Primary School, Kenton, Middlesex; 1952–1959: Harrow County Grammar School; 1959–1963: Selwyn College, Cambridge (Entrance Exhibition 1959, Scholarship 1961) 1960: First Class, Mathematical ...
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[7] Graph G {\displaystyle G} is vertex-critical if and only if for every vertex v {\displaystyle v} , there is an optimal proper coloring in which v {\displaystyle v} is a singleton color class. As Hajós (1961) showed, every k {\displaystyle k} -critical graph may be formed from a complete graph K k {\displaystyle K_{k}} by combining the ...
In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p.That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of p n copies of g, and not fewer, is equal to the identity element.