positive integer
The sum of the series of reciprocals of the cubic polynomials with triple non-positive integer root
... This contribution, which is a follow-up to author’s paper [1] dealing with the sums of the series of reciprocals of some quadratic polynomi- als, deals with the series of reciprocals of the cubic polynomials with triple ...
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Trace of Positive Integer Power of Real 2 × 2 Matrices
... any positive integer power of 2 × 2 real ...any positive integer power of 2 × 2 real matrix A, in the terms of Trace of A (TrA) and Determinant of A (DetA), which are based on definition of ...
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On the Positive Integer Solutions for a Diophantine Equation
... A Diophantine equation is a polynomial equation ( , , ⋯ , ) = 0 where the polynomial has integral coefficients and one is interested in solutions for which all the unknowns take integer values. For example, + ...
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Computation of Sample Mean Range of the Generalized Laplace Distribution
... a positive integer m into z parts, we mean all possible sets of z nonnegative integers that sum up to m ...nonnegative integer m into z nonnegative integers, is the same as to generate all of the ...
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Representations by certain octonary quadratic forms with coefficients 1, 5, or 25
... It is an important objective to determine the number of representations of a positive integer by certain quadratic forms in number theory.. Introduction.[r] ...
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On The Negative Pell Equation Y2 = 30x2 - 45
... non-square positive integer has been selected by various mathematicians for its non-trivial integer solutions when D takes different integral values[1- ...many integer solutions are ...
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On detection number of cycle related graphs
... are colored i (1 ≤ i ≤ k). The k-labeling c is detectable if every two adjacent vertices of G have distinct codes. The minimum positive integer k for which G has a detectable k-labeling is the detection ...
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Reduced invariants from cuspidal maps
... Besides the main component, which was defined in the Introduction, for every positive integer k and partition λ ⊢ d into k positive parts, there is an irreducible boundary component Dλ P[r] ...
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Seventh and Eighth Order Triangular Sum Labeling of Graphs
... ∀ = ∈ . The graph which admits such labeling is called a triangular sum graph. Definition 1.3. [5] A second order triangular number is a number obtained by adding all the squares of positive integer less ...
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Mining web graphs for recommendations identification for query suggestion with efficient search re-ranking
... When the graph is very large, a direct computation of e_R is very time consuming. We adopt its discrete approximation to compute the heat diffusion equation where P is a positive integer. In order to ...
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Analysis of the Relation between Sun Motion Law and the Change of Earth’s Environment
... the positive integer multiple relationship and if they have the least common multiple, Then there must be a stable variable force impulse so that the value of the variable force im- pulse of the moon, the ...
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NOT require the Axiom of Choice; for each xA we have constructed an EXPLICIT left inverse to f. — On the other hand, if we had simply said that one should pick some
... Finally, we shall prove the result when 0 < y < x. By property (2) in the notes there is a rational number r such that y < r < x. Write r = p/q, where p and q are both positivei; replacing p and q by M p and ...
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The Proof of Goldbach’s Conjecture on Prime Numbers
... even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since ...composite integer n strictly larger than 3, is located at the middle of the distance be- tween ...
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Partitioning the positive integers with higher order recurrences
... some choice positive integer for which 2.1 holds for For a given Stolarsky array, if k is the least determined, and identity 0, then these integers are uniquely of integers ck-, c_2,...,[r] ...
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Generalisation of a waiting time relation
... These elegant results, expressing the infinite series in closed form, can be generated form ( 1 O) for any positive integer value of R. This will be investigated in the next sectio[r] ...
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Observations on the Hyperbola, y2 = 14x2 + 16t, t >=0
... Also, we present infinitely many positive integer solutions in terms of Generalized Fibonacci sequences of numbers, Generalized Lucas sequences of numbers.. Keywords: Binary Quadratic In[r] ...
8
The number of Smallest parts of
... George E Andrews derived formula for the number of smallest parts of partitions of a positive integer n.. In this paper we derived the formula efficiently by using the concepts of r[r] ...
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Observations on the Hyperbola $y^2=182x^2+14$
... The binary quadratic equation of the form y 2 = Dx 2 + 1 where D non-square positive integer has been studied by various mathematicians for its non-trivial integral solutions. when D takes different ...
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The number of Smallest parts of of th j overpartitions n
... Sylvie Corteel and Jeremy Lovejoy [7] defined overpartitions and George E Andrews derived formula for the number of smallest parts of partitions of a positive integer n. In this paper the concepts of j ...
9
Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
... 1. Goldsmith. Pabst and Scott (5) proved a similar result without the property of being distinct units. The sum of unit of numbers of rings of quadratic field also discussed by Ashrafi and Vamos (6). Further result given ...
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