On the Set of Primitive Triples of Natural Numbers Satisfying the Diophantine Equation of Pythagor
Bagram Sibgatullovich Kochkarev
Issue:
Volume 5, Issue 1, June 2020
Pages:
1-3
Received:
31 October 2019
Accepted:
25 December 2019
Published:
23 April 2020
Abstract: The main task considered in the article is to find the condition primitive integer solutions of the Diophantine Pithagorean equation x2+y2=z2 It is known that for this purpose it is enough to find primive solution of x, y such that x is even and y is odd. In this paper, in particular, we proved that the z of a primitive solution is a Prime number of the form 4k+1. It is prove in this paper that any right triangle with integer side lengths has a hypotenuse equal to a Prime of the form 4k+1and we show with the help of the descent axiom how to find primitive solutions of x and y in this case. We divide the search for primitive solutions (x, y, z) of right triangles into two cases: 1) the hypotenuse of such triangles is a Prime number of the form 4k+1 and 2) the hypotenuse of such triangles is a composite number. In section 3 we use formulas known to the ancient Hindus to find primitive solutions of Pithagorean equations in cases where m and n2+n2 is an compaund number ending in 5. To find primes ending in 3 and 7, we refer the reader to our paper, which presents algorithms for constructing all primes and twin primes. The proposed paper also presents a generalization of Euclid's fundamental result on the infinity of the set of Primes, namely, it is shown that all twin primes are in residue classes (1, 3), (2, 4), (4, 1), and there are infinity many such twins.
Abstract: The main task considered in the article is to find the condition primitive integer solutions of the Diophantine Pithagorean equation x2+y2=z2 It is known that for this purpose it is enough to find primive solution of x, y such that x is even and y is odd. In this paper, in particular, we proved that the z of a primitive solution is a Prime number o...
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Application of Intuitionistic Fuzzy Soft Matrices for Disease Diagnosis
Rana Muhammad Zulqarnain,
Muhammad Saeed,
Muhammad Irfan Ahamad,
Sohaib Abdal,
Zeeshan Zafar,
Muhammad Aslam
Issue:
Volume 5, Issue 1, June 2020
Pages:
4-9
Received:
27 August 2020
Accepted:
18 September 2020
Published:
30 September 2020
Abstract: Decision Making is the best procedure to choose a superlative alternative from all feasible alternatives. Almost in all other issues, the overall number of criteria because decision making the general alternatives is pervasive. Nowadays decision making is a critical problem in every field of life. In some cases, we must deliberate membership unbiassed as the non- membership values for the suitable representation of an object in uncertain and indeterminate conditions that could not be handled by fuzzy sets nor by interval-valued fuzzy sets. To overcome these difficulties the notion of Intuitionistic fuzzy sets has been presented. In this paper, we study some basic concepts of fuzzy sets, soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic soft sets, intuitionistic fuzzy soft sets (IFSS), and intuitionistic fuzzy soft matrices (IFSM). Finally, in this research, we use the IFSM for disease diagnoses in patients who suffer from different diseases such as stomach ulcer and typhoid by using hypothetical data we conclude that patient p2 suffering stomach ulcer p2 and p3 patients suffering from typhoid.
Abstract: Decision Making is the best procedure to choose a superlative alternative from all feasible alternatives. Almost in all other issues, the overall number of criteria because decision making the general alternatives is pervasive. Nowadays decision making is a critical problem in every field of life. In some cases, we must deliberate membership unbias...
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