[PDF] Top 20 On some Diophantine equations
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On some Diophantine equations
... Now, let us examine all solutions of the following equations by using Diophantine equations given in Theorem , Theorem , Theorem and the divisibility rules of the sequences un an[r] ... See full document
12
A repulsion motif in Diophantine equations
... these equations was made by Siegel, who proved that a nonsingular plane cubic equation has only finitely many integral ...simple equations can have inordinately large integral solutions in comparison to the ... See full document
19
Modular and reciprocity approaches to a family of diophantine equations
... upon the theory of the modular approach to Diophantine equations. The ba- sic technique was previously developed by mathematicians like Hellegouarch [28], Frey [22], Mazur, Serre [36], and Ribet in the ... See full document
141
Applications of Continued Fractions in Cryptography and Diophantine Equations
... The theory of continued fractions has applications in cryptographic problems and in so- lution methods for Diophantine equations. We will first examine the basic properties of continued fractions such as ... See full document
46
All the Solutions of the Diophantine Equations (p + 1)^x – p^y = z^2 and p^y - (p + 1)^x = z^2 when p is Prime and x + y = 2, 3, 4
... The field of Diophantine equations is ancient, vast and no general method exists to decide whether a given Diophantine equation has any solutions, or how many solutions.. The literatur[r] ... See full document
5
Three special systems of double diophantine equations
... solutions. In this context, one may refer (Gopalan et al, 2014; Gopalan et al, 2016; Gopalan et al, 2016; Gopalan et al, 2016; Meena et al, 2016; Gopalan et al, 2016; Devibala et al, 2017). The above results motivated us ... See full document
5
On Solutions of the Diophantine Equations p^4 + q^4 = z^2 and p^4-q^4= z^2 when p and q are Primes
... of Diophantine equations is ancient, vast, and no general method exists to decide whether a given Diophantine equation has any solutions, or how many ...individual equations, rather than ... See full document
5
All the Solutions of the Diophantine Equations $p^x + p^y = z^2$ and $p^x - p^y = z^2$ when p≥2 is Prime
... The field of Diophantine equations is ancient, vast, and no general method exists to decide whether a given Diophantine equation has any solutions, or how many solutions.. [r] ... See full document
9
On Polynomials Solutions of Quadratic Diophantine Equations
... A Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers ...only. Diophantine problems have fewer equations than un- known variables and involve finding ... See full document
5
On a few Diophantine equations, in particular, Fermat's last theorem
... see some equations which have no solution at all, and you will come across some equations about which the only thing we know is that we know nothing about ...other Diophantine ... See full document
28
Superconformal Block Quivers, Duality Trees and Diophantine Equations
... the Diophantine equation as the Tits form of the quiver, Seiberg duality is seen as affine Weyl reflections in the space of roots, provides a representation- theoretic approach - complementing the usual geometric ... See full document
45
Diophantine equations and identities
... Some new third and fifth degree combinatorial identities are derived from units in algebraic number fields... KEY WORDS AND PHRASES..[r] ... See full document
23
On a class of diophantine equations
... The only remaining possibilities for more solutions are where X or Y ∈ {−4, −3, −2, −1, 0} where there are no nontrivial solutions and the proof is completed.. Finally note that 6 has 16[r] ... See full document
9
Lagrange, central norms, and quadratic Diophantine equations
... As is often the case, some results get rediscovered over time. In particular, some rather striking results of Lagrange are often recreated. For instance, in [6], a result pertain- ing to the Pell equation ... See full document
9
Gauss' algorithm for the solution of quadratic diophantine equations
... The nunber of reduced forms in a period of rJuced forms of determinantperiod of the classical continued fractio^ ii lf,"-n.*U"r of terms in the expansion of an appropriate quadratic irra[r] ... See full document
30
Observation on the Non-Homogeneous Binary Quadratic Diophantine Equation $5x^2-6y^2=5$
... quadratic Diophantine equations of the form ax 2 − by 2 = N , ( a , b , N ≠ 0 ) are rich in variety and have been analyzed by many mathematicians for their respective integer solutions for particular values ... See full document
8
A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$
... quadratic equations are rich in variety, one may search for the other choice of ternary quadratic Diophantine equations and determine their integer solutions along with suitable ... See full document
7
On the Hyperbola $2x^2-3y^2=23$
... quadratic Diophantine equations of the form ax 2 − by 2 = N , ( a , b , N ≠ 0 ) are rich in variety and have been analyzed by many mathematicians for their respective integer solutions for particular values ... See full document
9
The upper bound estimate of the number of integer points on elliptic curves y2=x3+p2rx
... Using some properties of Diophantine equations, we give a sharper upper bound estimate for Npr , the number of pairs of non-trivial integer points x, ±y on ... That is, we shall prove[r] ... See full document
6
On the Ternary Quadratic Diophantine Equation $3(x^2+y^2)-5xy+2(x+y)+4=15z^2$
... L.E.Dickson, History of Theory of Numbers and Diophantine Analysis, Dover Publications, New York 2005.. L.J.Mordell, Diophantine Equations, Academic Press, New York 1970.[r] ... See full document
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