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Meaning of "Diophantine equation" in the English dictionary

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DICTIONARY
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ETYMOLOGY OF THE WORD DIOPHANTINE EQUATION

After Diophantus, Greek mathematician of the 3rd century ad.
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Etymology is the study of the origin of words and their changes in structure and significance.
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PRONUNCIATION OF DIOPHANTINE EQUATION

Diophantine equation  [ˌdaɪəʊˈfæntaɪn] play
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GRAMMATICAL CATEGORY OF DIOPHANTINE EQUATION

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Diophantine equation is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES DIOPHANTINE EQUATION MEAN IN ENGLISH?

Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation in two or more unknowns such that only the integer solutions are searched or studied. A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and ask about the lattice points on it. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis. While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations was an achievement of the twentieth century.

Definition of Diophantine equation in the English dictionary

The definition of Diophantine equation in the dictionary is an equation in more than one variable and with integral coefficients, for which integral solutions are sought.

WORDS THAT RHYME WITH DIOPHANTINE EQUATION


adamantine
ˌædəˈmæntaɪn
amarantine
ˌæməˈræntaɪn
argentine
ˈɑːdʒənˌtaɪn
Bernstein
ˈbɜːnstaɪn
bisontine
bɪˈsɒntaɪn
cispontine
sɪsˈpɒntaɪn
Corybantine
ˌkɒrɪˈbæntaɪn
diamantine
ˌdaɪəˈmæntaɪn
Einstein
ˈaɪnstaɪn
elephantine
ˌɛlɪˈfæntaɪn
Frankenstein
ˈfræŋkɪnˌstaɪn
Holstein
ˈhəʊlstaɪn
Liechtenstein
ˈlɪktənˌstaɪn
Palestine
ˈpælɪˌstaɪn
stein
staɪn
tine
taɪn
transpontine
trænzˈpɒntaɪn
Tridentine
traɪˈdɛntaɪn
Tyne
taɪn
valentine
ˈvælənˌtaɪn

WORDS THAT BEGIN LIKE DIOPHANTINE EQUATION

Diomed
Diomede
Diomede Islands
Diomedes
Dion
Dione
Dionysia
Dionysiac
Dionysian
Dionysius
Dionysius Exiguus
Dionysius of Halicarnassus
Dionysius the Areopagite
Dionysos
Dionysus
Diophantus

WORDS THAT END LIKE DIOPHANTINE EQUATION

accreditation
action
administration
animation
application
association
certification
citation
combination
communication
confirmation
conversation
corporation
creation
decoration
destination
documentation
duration
education
evaluation
excitation

Synonyms and antonyms of Diophantine equation in the English dictionary of synonyms

SYNONYMS

Translation of «Diophantine equation» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF DIOPHANTINE EQUATION

Find out the translation of Diophantine equation to 25 languages with our English multilingual translator.
The translations of Diophantine equation from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «Diophantine equation» in English.

Translator English - Chinese

丢番图方程
1,325 millions of speakers

Translator English - Spanish

ecuación Diophantine
570 millions of speakers

English

Diophantine equation
510 millions of speakers

Translator English - Hindi

Diophantine समीकरण
380 millions of speakers
ar

Translator English - Arabic

المعادلة ديوفانتاين
280 millions of speakers

Translator English - Russian

диофантов уравнение
278 millions of speakers

Translator English - Portuguese

equação Diophantine
270 millions of speakers

Translator English - Bengali

ডায়োফ্যান্টাইন সমীকরণ
260 millions of speakers

Translator English - French

équation diophantienne
220 millions of speakers

Translator English - Malay

Persamaan Diophantine
190 millions of speakers

Translator English - German

Diophantische Gleichung
180 millions of speakers

Translator English - Japanese

ディオファントス方程式
130 millions of speakers

Translator English - Korean

디오 판 투스 방정식
85 millions of speakers

Translator English - Javanese

Persamaan Diophantine
85 millions of speakers
vi

Translator English - Vietnamese

Diophantine phương trình
80 millions of speakers

Translator English - Tamil

டைபோஃப்டின் சமன்பாடு
75 millions of speakers

Translator English - Marathi

डायोफंटिन समीकरण
75 millions of speakers

Translator English - Turkish

Diofant denklemi
70 millions of speakers

Translator English - Italian

equazione diofantea
65 millions of speakers

Translator English - Polish

równanie diofantyczne
50 millions of speakers

Translator English - Ukrainian

Діофантом рівняння
40 millions of speakers

Translator English - Romanian

ecuație diofantice
30 millions of speakers
el

Translator English - Greek

Diophantine εξίσωση
15 millions of speakers
af

Translator English - Afrikaans

Diophantine vergelyking
14 millions of speakers
sv

Translator English - Swedish

Diophantine ekvation
10 millions of speakers
no

Translator English - Norwegian

Diofantisk ligningen
5 millions of speakers

Trends of use of Diophantine equation

TRENDS

TENDENCIES OF USE OF THE TERM «DIOPHANTINE EQUATION»

The term «Diophantine equation» is normally little used and occupies the 144.239 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Little used
33
/100
The map shown above gives the frequency of use of the term «Diophantine equation» in the different countries.
Principal search tendencies and common uses of Diophantine equation
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «Diophantine equation».

FREQUENCY OF USE OF THE TERM «DIOPHANTINE EQUATION» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «Diophantine equation» during the past 500 years. Its implementation is based on analysing how often the term «Diophantine equation» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about Diophantine equation

EXAMPLES

10 ENGLISH BOOKS RELATING TO «DIOPHANTINE EQUATION»

Discover the use of Diophantine equation in the following bibliographical selection. Books relating to Diophantine equation and brief extracts from same to provide context of its use in English literature.
1
Diophantine equations
Diophantine equations
Louis Joel Mordell, 1969
2
Time-varying Feedback Systems Design Via Diophantine ...
Diophantine equation plays an important role in the design and synthesis of feedback compensators.
Shr-Hua Wu, 2007
3
DIOPHANTINE EQUATION, THE FIELD OF BLOOD
MICHAEL TAYLOR. DIOPHANTINE EQUATION, THE FIELD OF BLOOD '\\\":~. MICHAEL TAYLOR DIOPHANTINE EQUATION, THE FIELD OF BLOOD THE INDETERMINATEPOLYNOMIAL EQUATION WITH. Front Cover.
MICHAEL TAYLOR
4
Handbook of Discrete and Combinatorial Mathematics
An equation with the added proviso that the solutions must be integers (or must belong to some other specified countable set, such as the set of rational numbers ) is called a diophantine equation. This name comes from the ancient Greek ...
Kenneth H. Rosen, 1999
5
A Transition to Advanced Mathematics : A Survey Course: A ...
Example 3.3.2 We examine two equations—one is Diophantine with positive integer solutions, and one is not. • x − y = 0 is a Diophantine equation with infinitely many solutions x = y = 1, x = y = 2, and so on; that is, every pair of integers with x ...
William Johnston Associate Dean of the College and Stodghill Professor of Mathematics Centre College, Alex McAllister Associate Professor of Mathematics Centre College, 2009
6
Geometric Theorems, Diophantine Equations, and Arithmetic ...
4 The Diophantine equation xn + yn = xpyqz (where p + q = n) . . . . . . . 64 1 +1 +... +1 =1 5 On the diophantine equation . . . . . . . . . . 65 x1 x2 xn xn+1 6 On the diophantine equation x1! + x2! + ... + xn! = xn+1! . . . . . . . . . . 68 7 The diophantine  ...
J. Sándor, 2002
7
Unsolved Problems in Number Theory
Chen Xi-Geng & Le Mao-Hua, The Diophantine equation (xm - 1) (xm" - 1 ) = y2, Huaihua Shizhuan Xuebao, 30(2001) 11-12; MR 97k:11045. Mihai Cipu, A bound for the solutions of the Diophantine equation Dix2 + D? = 4y", Proc.
Richard Guy, 2004
8
Logic, Methodology and Philosophy of Science: Proceedings of ...
That is, to every recursively enumerable set S of positive integers, there is an exponential Diophantine equation E(s,ult . . .,um) such that s eS if and only if E(s, ult . . ., um) is solvable in positive integers. The proof of this result is constructive.
Ernest Nagel, Patrick Suppes, Alfred Tarski, 1962
9
Index to Mathematical Problems, 1980-1984
The Diophantine equation 8x3 - 21x2y + 35xj/2 - 83y3 = z3 has the obvious solutions (x, y, z) = (k, 0, 2k), where k is an integer. Find at least two solutions for which y ^ 0. CRUX 719. by Noam D. Elkies Are there positive integers x, y and z such ...
Stanley Rabinowitz, 1992
10
The Algorithmic Resolution of Diophantine Equations: A ...
On a quartic diophantine equation. Proc. Edin. Math. Soc., 39, 97-114, 1996. [194 ] J.T. Tate. The arithmetic of elliptic curves. Invent. Math, 23, 179-206, 1974. [195] E. Thomas. Complete solutions to a family of cubic diophantine equations.
Nigel P. Smart, 1998

3 NEWS ITEMS WHICH INCLUDE THE TERM «DIOPHANTINE EQUATION»

Find out what the national and international press are talking about and how the term Diophantine equation is used in the context of the following news items.
1
Another Reason to Love the Number Seven
For example, if we look for Pythagorean triples, integers that satisfy the equation a2+b2=c2, we're looking at a Diophantine equation. Logically ... «Scientific American, Sep 14»
2
Hyperbolic homogeneous polynomials, oh my!
This is a linear Diophantine equation." Number theory also plays an important role in encryption. "Every time one visits a website with an https:// ... «Phys.Org, Apr 14»
3
Mayfield Man Uses Lego Art To Show The Importance Of Math
He used a diophantine equation to make the two shapes fit. And the tower's telltale lean? That was also a matter of math. Gugick calculated ... «Patch.com, Mar 13»

REFERENCE
« EDUCALINGO. Diophantine equation [online]. Available <https://educalingo.com/en/dic-en/diophantine-equation>. Apr 2024 ».
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