Academic literature on the topic 'Diophantine equations'
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Journal articles on the topic "Diophantine equations"
Bruno, Alexander Dmitrievich. "From Diophantine approximations to Diophantine equations." Keldysh Institute Preprints, no. 1 (2016): 1–20. http://dx.doi.org/10.20948/prepr-2016-1.
Full textAggarwal, S., and S. Kumar. "On the Exponential Diophantine Equation (132m) + (6r + 1)n = z2." Journal of Scientific Research 13, no. 3 (September 1, 2021): 845–49. http://dx.doi.org/10.3329/jsr.v13i3.52611.
Full textSrinivasa Rao, K., T. S. Santhanam, and V. Rajeswari. "Multiplicative Diophantine equations." Journal of Number Theory 42, no. 1 (September 1992): 20–31. http://dx.doi.org/10.1016/0022-314x(92)90105-x.
Full textChoudhry, Ajai. "Symmetric Diophantine Equations." Rocky Mountain Journal of Mathematics 34, no. 4 (December 2004): 1281–98. http://dx.doi.org/10.1216/rmjm/1181069800.
Full textHajdu, L., and Á. Pintér. "Combinatorial Diophantine equations." Publicationes Mathematicae Debrecen 56, no. 3-4 (April 1, 2000): 391–403. http://dx.doi.org/10.5486/pmd.2000.2179.
Full textCohn, J. H. E. "Twelve diophantine equations." Archiv der Mathematik 65, no. 2 (August 1995): 130–33. http://dx.doi.org/10.1007/bf01270690.
Full textTahiliani, Dr Sanjay. "More on Diophantine Equations." International Journal of Management and Humanities 5, no. 6 (February 28, 2021): 26–27. http://dx.doi.org/10.35940/ijmh.l1081.025621.
Full textVălcan, Teodor Dumitru. "From Diophantian Equations to Matrix Equations (III) - Other Diophantian Quadratic Equations and Diophantian Equations of Higher Degree." Educatia 21, no. 25 (November 30, 2023): 167–77. http://dx.doi.org/10.24193/ed21.2023.25.18.
Full textAcewicz, Marcin, and Karol Pąk. "Basic Diophantine Relations." Formalized Mathematics 26, no. 2 (July 1, 2018): 175–81. http://dx.doi.org/10.2478/forma-2018-0015.
Full textBiswas, D. "Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?" Journal of Scientific Research 14, no. 3 (September 1, 2022): 861–65. http://dx.doi.org/10.3329/jsr.v14i3.58535.
Full textDissertations / Theses on the topic "Diophantine equations"
Lee, Ellyn Jay. "Studies on diophantine equations." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239075.
Full textMabaso, Automan Sibusiso. "Some exponential diophantine equations." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85587.
Full textENGLISH ABSTRACT: The aim of this thesis is to study some methods used in solving exponential Diophan- tine equations. There is no generic method or algorithm that can be used in solving all Diophantine equations. The main focus for our study will be solving the exponential Dio- phantine equations using the modular approach and the linear forms in two logarithms approach.
AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om sommige metodes te bestudeer om sekere Diophantiese vergelykings op te los. Daar is geen metode wat alle Diophantiese vergelykings kan oplos nie. Die fokus van os studie is hoofsaaklik om eksponensiele Diophantiese vergelykings op te los met die modul^ere metode en met die metode van line^ere vorms in twee logaritmes.
Bartolomé, Boris. "Diophantine equations and cyclotomic fields." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0104/document.
Full textThis thesis examines some approaches to address Diophantine equations, specifically we focus on the connection between the Diophantine analysis and the theory of cyclotomic fields.First, we propose a quick introduction to the methods of Diophantine approximation we have used in this research work. We remind the notion of height and introduce the logarithmic gcd.Then, we address a conjecture, made by Thoralf Skolem in 1937, on an exponential Diophantine equation. For this conjecture, let K be a number field, α1 ,…, αm , λ1 ,…, λm non-zero elements in K, and S a finite set of places of K (containing all the infinite places) such that the ring of S-integersOS = OK,S = {α ∈ K : |α|v ≤ 1 pour les places v ∈/ S}contains α1 , . . . , αm , λ1 , . . . , λm α1-1 , . . . , αm-1. For each n ∈ Z, let A(n)=λ_1 α_1^n+⋯+λ_m α_m^n∈O_S. Skolem suggested [SK1] :Conjecture (exponential local-global principle). Assume that for every non zero ideal a of the ring O_S, there exists n ∈ Z such that A(n) ≡0 mod a. Then, there exists n ∈ Z such that A(n)=0.Let Γ be the multiplicative group generated by α1 ,…, αm. Then Γ is the product of a finite abelian group and a free abelian group of finite rank. We prove that the conjecture is true when the rank of Γ is one.After that, we generalize a result previously published by Abouzaid ([A]). Let F(X,Y) ∈ Q[X,Y] be an irreducible Q-polynomial. In 2008, Abouzaid [A] proved the following theorem:Theorem (Abouzaid). Assume that (0,0) is a non-singular point of the plane curve F(X,Y) = 0. Let m = degX F, n = degY F, M = max{m, n}. Let ε satisfy 0 < ε < 1. Then for any solution (α,β) ∈ Q ̅2 of F(X,Y) = 0, we have eithermax{h(α), h(β)} ≤ 56M8ε−2hp(F) + 420M10ε−2 log(4M),ormax{|h(α) − nlgcd(α, β)|,|h(β) − mlgcd(α, β)|} ≤ εmax{h(α), h(β)}++ 742M7ε−1hp(F) + 5762M9ε−1log(2m + 2n)However, he imposed the condition that (0, 0) be a non-singular point of the plane curve F(X,Y) = 0. Using a somewhat different version of Siegel’s “absolute” lemma and of Eisenstein’s lemma, we could remove the condition and prove it in full generality. We prove the following theorem:Theorem. Let F(X,Y) ∈ Q ̅[X,Y] be an absolutely irreducible polynomial satisfying F(0,0)=0. Let m=degX F, n=degY F and r = min{i+j:(∂^(i+j) F)/(∂^i X∂^j Y)(0,0)≠0}. Let ε be such that 0 < ε < 1. Then, for all (α, β) ∈ Q ̅2 such that F(α,β) = 0, we have eitherh(α) ≤ 200ε−2mn6(hp(F) + 5)or|(lgcd(α,β))/r-h(α)/n|≤1/r (εh(α)+4000ε^(-1) n^4 (h_p (F)+log(mn)+1)+30n^2 m(h_p (F)+log(mn) ))Then, we give an overview of the tools we have used in cyclotomic fields. We try there to develop a systematic approach to address a certain type of Diophantine equations. We discuss on cyclotomic extensions and give some basic but useful properties, on group-ring properties and on Jacobi sums.Finally, we show a very interesting application of the approach developed in the previous chapter. There, we consider the Diophantine equation(1) Xn − 1 = BZn,where B ∈ Z is understood as a parameter. Define ϕ∗(B) := ϕ(rad (B)), where rad (B) is the radical of B, and assume that (2) (n, ϕ∗(B)) = 1.For a fixed B ∈ N_(>1)we let N(B) = {n ∈ N_(>1) | ∃ k > 0 such that n|ϕ∗(B)}. If p is an odd prime, we shall denote by CF the combined condition requiring thatI The Vandiver Conjecture holds for p, so the class number h+ of the maximal real subfield of the cyclotomic field Q[ζp ] is not divisible by p.II We have ir>(p) < √p − 1, in other words, there is at most √p − 1 odd integers k < p such that the Bernoulli number Bk ≡ 0 mod p. [...]
Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.
Full textSmart, Nigel Paul. "The computer solution of diophantine equations." Thesis, University of Kent, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315089.
Full textLong, Rachel Louise. "The algorithmic solution of simultaneous diophantine equations." Thesis, Oxford Brookes University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444340.
Full textBaczkowski, Daniel M. "Diophantine Equations Involving Arithmetic Functions of Factorials." Miami University / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258.
Full textAkhtari, Shabnam. "Thue equations and related topics." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1288.
Full textSchindler, Damaris. "On diophantine equations involving norm forms and bihomogeneous forms." Thesis, University of Bristol, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.601162.
Full textIbrahim, Mostafa. "Modular and reciprocity approaches to a family of diophantine equations." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/2761/.
Full textBooks on the topic "Diophantine equations"
Schmidt, Wolfgang M. Diophantine Approximations and Diophantine Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0098246.
Full textSchmidt, Wolfgang M. Diophantine approximations and diophantine equations. Berlin: Springer, 1996.
Find full textDiophantine approximations and diophantine equations. Berlin: Springer-Verlag, 1991.
Find full textAndreescu, Titu, and Dorin Andrica. Quadratic Diophantine Equations. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-0-387-54109-9.
Full textSprindžuk, Vladimir G. Classical Diophantine Equations. Edited by Ross Talent. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0073786.
Full textR, Tijdeman, ed. Exponential diophantine equations. Cambridge [Cambridgeshire]: Cambridge University Press, 1986.
Find full textShorey, T. N. Exponential diophantine equations. Cambridge: Cambridge University Press, 2008.
Find full textSprindzhuk, V. G. Classical diophantine equations. Berlin: Springer-Verlag, 1993.
Find full text1955-, Silverman Joseph H., ed. Diophantus and diophantine equations. [Washington, DC]: Mathematical Association of America, 1997.
Find full textWeger, B. M. M. Algorithms for diophantine equations. Amsterdam: Stichting Mathematisch Centrum, 1989.
Find full textBook chapters on the topic "Diophantine equations"
Ireland, Kenneth, and Michael Rosen. "Diophantine Equations." In A Classical Introduction to Modern Number Theory, 269–96. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_17.
Full textAndreescu, Titu, and Dorin Andrica. "Diophantine Equations." In Number Theory, 1–17. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/b11856_19.
Full textAndreescu, Titu, and Dorin Andrica. "Diophantine Equations." In Number Theory, 1–21. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/b11856_8.
Full textCaminha Muniz Neto, Antonio. "Diophantine Equations." In Problem Books in Mathematics, 193–207. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77977-5_7.
Full textFaltings, Gerd. "Diophantine Equations." In Mathematics Unlimited — 2001 and Beyond, 449–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56478-9_21.
Full textGuy, Richard K. "Diophantine Equations." In Unsolved Problems in Number Theory, 139–98. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4899-3585-4_5.
Full textSchroeder, Manfred R. "Diophantine Equations." In Number Theory in Science and Communication, 95–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-22246-1_7.
Full textGuy, Richard K. "Diophantine Equations." In Unsolved Problems in Number Theory, 209–310. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-26677-0_5.
Full textSchroeder, Manfred R. "Diophantine Equations." In Number Theory in Science and Communication, 102–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03430-9_7.
Full textEffinger, Gove, and Gary L. Mullen. "Diophantine Equations." In Elementary Number Theory, 139–64. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003193111-9.
Full textConference papers on the topic "Diophantine equations"
Riemel, Tomáš. "SPECIAL EXPONENTIAL DIOPHANTINE EQUATIONS." In 15th annual International Conference of Education, Research and Innovation. IATED, 2022. http://dx.doi.org/10.21125/iceri.2022.0270.
Full textȚARĂLUNGĂ, Boris. "About solutions of some non – linear Diophantine equations." In Ştiință și educație: noi abordări și perspective. "Ion Creanga" State Pedagogical University, 2023. http://dx.doi.org/10.46727/c.v3.24-25-03-2023.p293-298.
Full textHu, Cheng-Feng, and Fung-Bao Liu. "Solving System of Fuzzy Diophantine Equations." In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2008. http://dx.doi.org/10.1109/fskd.2008.111.
Full textAvdyev, M. "THE DIOPHANTINE EQUATION FROM THE EYE OF PHYSICIST." In X Международная научно-практическая конференция "Культура, наука, образование: проблемы и перспективы". Нижневартовский государственный университет, 2022. http://dx.doi.org/10.36906/ksp-2022/57.
Full textHe Kong, Bin Zhou, and Mao-Rui Zhang. "A Stein equation approach for solutions to the Diophantine equations." In 2010 Chinese Control and Decision Conference (CCDC). IEEE, 2010. http://dx.doi.org/10.1109/ccdc.2010.5498658.
Full textCipu, Mihai. "Groebner Bases and Solutions to Diophantine Equations." In 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE, 2008. http://dx.doi.org/10.1109/synasc.2008.13.
Full textWalsh, P. G., and Takao Komatsu. "Recent Progress on Certain Quartic Diophantine Equations." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841908.
Full textBerkholz, Christoph, and Martin Grohe. "Linear Diophantine Equations, Group CSPs, and Graph Isomorphism." In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2017. http://dx.doi.org/10.1137/1.9781611974782.21.
Full textMiyazaki, Takafumi, Masaaki Amou, and Masanori Katsurada. "Exceptional cases of Terai’s conjecture on Diophantine equations." In DIOPHANTINE ANALYSIS AND RELATED FIELDS 2011: DARF - 2011. AIP, 2011. http://dx.doi.org/10.1063/1.3630043.
Full textDhurga, C. Kanaga. "Reflecting the application of Diophantine equations in chemistry." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108562.
Full textReports on the topic "Diophantine equations"
Jain, Himanshu, Edmund M. Clarke, and Orna Grumberg. Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada476801.
Full textOsipov, Gennadij Sergeevich, Natella Semenovna Vashakidze, and Galina Viktorovna Filippova. Fundamentals of solving linear Diophantine equations with two unknowns. Постулат, 2018. http://dx.doi.org/10.18411/postulat-2018-2-37.
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