ConseggioLigure/seed-instruct-lij-eng huggingface dataset:
Traduxi da-o zeneise à l’ingleise:
Pe fâ un exempio, i computer digitali peuan deuviâ torna i circuiti d’addiçion existenti e economizzâ quelli azzontivi pe implementâ unna sottraçion, deuviando o metodo do completemento à doî pe representâ i inversci additivi, che son ben ben façili da implementâ in sce hardware (negaçion).
A traduçion in ingleise do testo a l’é:
For example, digital computers can reuse existing adding-circuitry and save additional circuits for implementing a subtraction, by employing the method of two's complement for representing the additive inverses, which is extremely easy to implement in hardware (negation).
Comm’à l’é a traduçion ingleise de sto testo?
A moltiplicaçion ascì a combiña doî numeri inte un numero solo, o produto.
A traduçion in ingleise do testo a l’é:
Multiplication also combines two numbers into a single number, the product.
Traduxi in lengua ingleise:
Tutti i dividdendi, divixi pe-o zero, son indefinii.
A traduçion in ingleise do testo a l’é:
Any dividend divided by zero is undefined.
Traduxi in ingleise:
O teorema fondamentale de l’aritmetica o l’é stæto provou pe-o primmo da Carl Friedrich Gauss.
A traduçion in ingleise do testo a l’é:
The fundamental theorem of arithmetic was first proven by Carl Friedrich Gauss.
Traduxi sto testo da-o ligure à l’ingleise:
A nottaçion poxiçionale (conosciua ascì comme «nottaçion di valoî de poxiçion») a se referisce a-a representaçion ò a-a codifica di numeri, pe mezo do mæximo scimbolo pe-i varri ordini de grandessa (comme «o pòsto de unitæ», «o pòsto de dëxeñe», «pòsto de çentenæa») e con un ponto reixe, pe mezo de quelli mæximi scimboli pe representâ e fraçioin (comme «o pòsto de dexime parte», «o pòsto di çenteximi»).
A traduçion in ingleise do testo a l’é:
Positional notation (also known as "place-value notation") refers to the representation or encoding of numbers using the same symbol for the different orders of magnitude (e.g., the "ones place", "tens place", "hundreds place") and, with a radix point, using those same symbols to represent fractions (e.g., the "tenths place", "hundredths place").
Traduxi da-o ligure à l’ingleise:
O resultato o ve carcolou con l’azzonze repetuo de giffre sence da tutti i numeri ch’òccupan a mæxima poxiçion, da-a drita a-a manciña.
A traduçion in ingleise do testo a l’é:
The result is calculated by the repeated addition of single digits from each number that occupies the same position, proceeding from right to left.
Traduxi da-o ligure à l’ingleise:
A giffra ciù a-a drita o l’é o valô da poxiçion do momento e o resultato pe l’addiçion succesciva de giffre a-a manciña a l’aumenta o valô da segonda giffra (ciù a-a manciña), ch’a l’é sempre un (se no zero).
A traduçion in ingleise do testo a l’é:
The rightmost digit is the value for the current position, and the result for the subsequent addition of the digits to the left increases by the value of the second (leftmost) digit, which is always one (if not zero).
Traduxi in lengua ingleise:
Unna tabella de moltiplicaçion da dexe righe e dexe colònne a l’elenca i resultati pe tutte e cobbie de giffre.
A traduçion in ingleise do testo a l’é:
A multiplication table with ten rows and ten columns lists the results for each pair of digits.
Traduxi in ingleise:
De tecniche scimili existan pe-a sottraçion e a divixon.
A traduçion in ingleise do testo a l’é:
Similar techniques exist for subtraction and division.
Traduxi sto testo da-o ligure à l’ingleise:
Inta terminologia matematica sta caratteristica a l’é definia «ciösua», e l’elenco preçedente o l’é definio comme .
A traduçion in ingleise do testo a l’é:
In mathematical terminology, this characteristic is defined as closure, and the previous list is described as .
Traduxi sto testo da-o zeneise à l’ingleise:
O totale, inta colònna di penny, o l’é 25.
A traduçion in ingleise do testo a l’é:
The total in the pence column is 25.
Traduxi sto testo da-o ligure à l’ingleise:
St’operaçion a ven repetua deuviando i valoî da colònna di scellin, pe azzonze dapeu o valô stæto reportou inta colònna di penni.
A traduçion in ingleise do testo a l’é:
This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column.
Traduxi in lengua ingleise:
Un tipico libbretto ch’o l’arrivava a-e 150 pagine o tabulava di moltipli «da un à dexemia a-i prexi da un farthing à unna sterliña».
A traduçion in ingleise do testo a l’é:
One typical booklet that ran to 150 pages tabulated multiples "from one to ten thousand at the various prices from one farthing to one pound".
Comm’à l’é a traduçion ingleise de sto testo?
Sto studio o l’é ciammou de vòtte co-o nomme de «algorismo».
A traduçion in ingleise do testo a l’é:
This study is sometimes known as algorism.
Traduxi sto testo da-o ligure à l’ingleise:
L’aritmetica a l’é stæta deuviâ da-i studioxi islamichi co-a finanlitæ de mostrâ e applicaçioin di decreti ligæ à Zakat e Irth.
A traduçion in ingleise do testo a l’é:
Also, arithmetic was used by Islamic Scholars in order to teach application of the rulings related to Zakat and Irth.
Ti peu tradue sto testo in ingleise?
L’addiçion (pe-o sòlito representâ da-o scimbolo relativo) a l’é uña de operaçion a-a base de l’aritmetica; e atre træ son a sottraçioin, a moltiplicaçion e a divixon.
A traduçion in ingleise do testo a l’é:
Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.
Traduxi da-o ligure à l’ingleise:
Inte l’algebra, unn’atra ramma da matematica, l’addiçion a se peu realizzâ ascì pe di oggetti astræti comme vettoî, matrixe, sottospaçi e sottogruppi.
A traduçion in ingleise do testo a l’é:
In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Traduxi in lengua ingleise:
Pe mezo do suffisso gerundivo -nd s’ottëgne addend ‘cösa da azzonze’.
A traduçion in ingleise do testo a l’é:
Using the gerundive suffix -nd results in "addend", "thing to be added".
Ti peu tradue sto testo in ingleise?
Sum e summand, in ingleise, ne vëgnan da-o sostantivo latin summa ‘a çimma’ e da-o verbo conligou summare.
A traduçion in ingleise do testo a l’é:
"Sum" and "summand" derive from the Latin noun summa "the highest, the top" and associated verb summare.
Traduxi sto testo da-o zeneise à l’ingleise:
I termini ciù tardi de l’ingleise medio, adden e adding, en stæti portæ inta lengua de gente da Chaucer.
A traduçion in ingleise do testo a l’é:
The later Middle English terms "adden" and "adding" were popularized by Chaucer.
Traduxi in lengua ingleise:
Giusto pe fâ un exempio, l’esprescion a + b + c a doviæ ëse definia comme (a + b) + c ò a + (b + c)?
A traduçion in ingleise do testo a l’é:
As an example, should the expression a + b + c be defined to mean (a + b) + c or a + (b + c)?
Traduxi in ingleise:
Sciña çerti animæ a-o de feua de l’òmmo dan à divedde unna capaçitæ limitâ pe fâ de addiçioin, comme i primati.
A traduçion in ingleise do testo a l’é:
Even some nonhuman animals show a limited ability to add, particularly primates.
Ti peu tradue sto testo in ingleise?
Con ancon ciù tanta esperiensa, i figgeu imprendan à fâ de somme ciù a-a lesta pe mezo da propietæ commutativa de l’addiçion co-o contâ da-o numero ciù grande, inte sto caxo comensando da-o trei e contando «quattro, çinque».
A traduçion in ingleise do testo a l’é:
With additional experience, children learn to add more quickly by exploiting the commutativity of addition by counting up from the larger number, in this case, starting with three and counting "four, five."
Traduxi in ingleise:
Zero: da-o momento che o zero o l’é l’identitæ additiva, azzonze un zero no cangia o resultato.
A traduçion in ingleise do testo a l’é:
Zero: Since zero is the additive identity, adding zero is trivial.
Traduxi in ingleise:
Un o l’allinia doe fraçioin deximæ uña in çimma à l’atra, co-o ponto deximâ inta mæxima poxiçion.
A traduçion in ingleise do testo a l’é:
One aligns two decimal fractions above each other, with the decimal point in the same location.
Quæ a l’é a traduçion ingleise de sto testo?
Se i addendi son a lestixe de rotaçion de doî erbi, se peuan sommâ con un differençiale.
A traduçion in ingleise do testo a l’é:
If the addends are the rotation speeds of two shafts, they can be added with a differential.
Traduxi sto testo in ingleise:
O deuviava un meccanismo de traspòrto ascistio da-a gravitæ.
A traduçion in ingleise do testo a l’é:
It made use of a gravity-assisted carry mechanism.
Quæ a l’é a traduçion ingleise de sto testo?
Pe sottrae, l’operatô o l’aiva da deuviâ o complemento de carcolatoa de Pascan, ch’a domandava tanti pasci comme unn’addiçion.
A traduçion in ingleise do testo a l’é:
To subtract, the operator had to use the Pascal's calculator's complement, which required as many steps as an addition.
Ti peu tradue sto testo in ingleise?
Tanto e pòrte XOR comme quelle AND en façile da realizzâ in lògica digitale, ch’a permette a realizzaçioin de çircuiti d’addiçion completi che, à seu vòtta, peuan vegnî combinæ inte de operaçioin lògiche ciù complesse.
A traduçion in ingleise do testo a l’é:
Both XOR and AND gates are straightforward to realize in digital logic allowing the realization of full adder circuits which in turn may be combined into more complex logical operations.
Traduxi in ingleise:
L’overflow aritmetico imprevisto a l’é unna raxon pe di erroî de programmaçion ch’a s’attreuva assæ de lengê.
A traduçion in ingleise do testo a l’é:
Unanticipated arithmetic overflow is a fairly common cause of program errors.
Traduxi da-o ligure à l’ingleise:
Piggiâ a-a lettia, a definiçion stæta mensunâ de d’ato a l’é unn’applicaçion do teorema de recorscion in sce l’insemme parçialmente ordinou N2.
A traduçion in ingleise do testo a l’é:
Taken literally, the above definition is an application of the recursion theorem on the partially ordered set N2.
Ti peu tradue sto testo in ingleise?
Se a ò b o l’é pægio a-o zero, beseugna trattâli comme de identitæ.
A traduçion in ingleise do testo a l’é:
If either a or b is zero, treat it as an identity.
Comm’à l’é a traduçion ingleise de sto testo?
Chì o semigruppo o l’é formou da-i numeri naturali e o gruppo o l’é o gruppo additivo di intreghi.
A traduçion in ingleise do testo a l’é:
Here, the semigroup is formed by the natural numbers and the group is the additive group of integers.
Traduxi in ingleise:
A propietæ commutativa e assoçiativa de l’addiçion reale en immediæ; se se definisce o numero reale 0 comme l’insemme di raçionali negativi se vedde de lengê l’identitæ additiva.
A traduçion in ingleise do testo a l’é:
The commutativity and associativity of real addition are immediate; defining the real number 0 to be the set of negative rationals, it is easily seen to be the additive identity.
Traduxi sto testo da-o ligure à l’ingleise:
Beseugna demostrâ che st’operaçion a l’é ben definia, trattandose de sequense co-Cauchy.
A traduçion in ingleise do testo a l’é:
One must prove that this operation is well-defined, dealing with co-Cauchy sequences.
Traduxi sto testo da-o ligure à l’ingleise:
L’insemme di numeri intreghi mòdolo 2 o l’à solo che doî elementi: l’operaçion d’addiçion ch’o l’eredita a l’é conosciua, inta lògica booleaña, comme fonçion «exclusive or».
A traduçion in ingleise do testo a l’é:
The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function.
Traduxi sto testo da-o ligure à l’ingleise:
Questi dan doe generalizzaçion despæge de l’addiçion de numeri naturali a-o transinfinio.
A traduçion in ingleise do testo a l’é:
These give two different generalizations of addition of natural numbers to the transfinite.
Traduxi sto testo da-o ligure à l’ingleise:
Gh’é ancon ciù tante generalizzaçioin inta moltiplicaçion che inte l’addiçion.
A traduçion in ingleise do testo a l’é:
There are even more generalizations of multiplication than addition.
Traduxi sto testo in ingleise:
Defæti, se doî numeri no negativi a e b en despægi pe grandessa, aloa a seu somma a l’é pöcassæ pægia a-o seu mascimo.
A traduçion in ingleise do testo a l’é:
In fact, if two nonnegative numbers a and b are of different orders of magnitude, then their sum is approximately equal to their maximum.
Traduxi da-o zeneise à l’ingleise:
O comprende l’idea da somma de un numero sencio, ch’o l’é lê mæximo, e a somma veua, ch’a l’é pægia do zero.
A traduçion in ingleise do testo a l’é:
It includes the idea of the sum of a single number, which is itself, and the empty sum, which is zero.
Ti peu tradue sto testo in ingleise?
L’integraçion a l’é unna speçie de «sommatöia» in sce un continuo ò, con ciù precixon e in generale, in sce un collettô differençiabile.
A traduçion in ingleise do testo a l’é:
Integration is a kind of "summation" over a continuum, or more precisely and generally, over a differentiable manifold.
Traduxi sto testo da-o zeneise à l’ingleise:
E combinaçioin lineare an unna particolare utilitæ inte quelli contesti donde l’azzonta diretta a l’anieiva contra à quarche regola de normalizzaçion, comme a mescciua de strategie inta teoria di zeughi ò a sorvepoxiçion di stati inta mecanica quantistica.
A traduçion in ingleise do testo a l’é:
Linear combinations are especially useful in contexts where straightforward addition would violate some normalization rule, such as mixing of strategies in game theory or superposition of states in quantum mechanics.
Quæ a l’é a traduçion ingleise de sto testo?
A divixon a l’é uña de quattro operaçioin de base de l’aritmetica, saieiva à dî e mainee che permettan de combinâ di numeri pe cavâne di atri.
A traduçion in ingleise do testo a l’é:
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.
Traduxi sto testo in ingleise:
Quelli pe-i quæ se definisce unna divixon euclidea (con do resto) piggian o nomme de dominni euclidëi e comprendan di anelli polinomiali inte un indeterminou (che definiscian moltiplicaçion e addiçion in sce de formole con unna variabile solo).
A traduçion in ingleise do testo a l’é:
Those in which a Euclidean division (with remainder) is defined are called Euclidean domains and include polynomial rings in one indeterminate (which define multiplication and addition over single-variabled formulas).
Quæ a l’é a traduçion ingleise de sto testo?
Sto segno de divixon o se deuvia da solo ascì pe representâ a mæxima operaçion de divixon, comme etichetta in sce un pommello de unna carcolatoa.
A traduçion in ingleise do testo a l’é:
This division sign is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.
Traduxi da-o zeneise à l’ingleise:
A distribuçion d’oggetti despægi inte tutti i gii de condivixon pe tutte e porçioin a pòrta à l’idea de chunking, unna forma de divixon donde se sottrae de forma repetua di moltipi do divisô da-o dividdendo mæximo.
A traduçion in ingleise do testo a l’é:
Distributing the objects several at a time in each round of sharing to each portion leads to the idea of 'chunking' a form of division where one repeatedly subtracts multiples of the divisor from the dividend itself.
Traduxi in ingleise:
Unna persoña a peu deuviâ e tabelle di logaritmi pe dividde doî numeri, co-o sottrae i logaritmi di doî numeri, e dapeu ammiando l’antilogaritmo do resultato.
A traduçion in ingleise do testo a l’é:
A person can use logarithm tables to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result.
Quæ a l’é a traduçion ingleise de sto testo?
Çerti lenguaggi de programmaçion, comme o C, trattan a divixon di numeri intreghi comme into caxo 5 mensunou chì in çimma; donca a respòsta a l’é un numero intrego.
A traduçion in ingleise do testo a l’é:
Some programming languages, such as C, treat integer division as in case 5 above, so the answer is an integer.
Traduxi da-o zeneise à l’ingleise:
Do mæximo, a divixon drita de b pe a (scrita ) a l’é a soluçion y de l’equaçion.
A traduçion in ingleise do testo a l’é:
Similarly, right division of b by a (written ) is the solution y to the equation .
Traduxi da-o ligure à l’ingleise:
Di exempi comprendan l’algebra de matrixe e quella di quaternioin.
A traduçion in ingleise do testo a l’é:
Examples include matrix algebras and quaternion algebras.
Ti peu tradue sto testo in ingleise?
Se unn’esprescion comme questa a ven digitâ inte unna carcolatoa s’ottëgne un messaggio d’errô.
A traduçion in ingleise do testo a l’é:
Entry of such an expression into most calculators produces an error message.
Traduxi da-o zeneise à l’ingleise:
Da-o momento che sta sostituçion a redue o ciù grande di doî numeri, co-a repetiçion de sto processo s’ottëgne de cobbie de numeri succescivamente ciù piccin fin à quande i doî numeri vëgnan pægi.
A traduçion in ingleise do testo a l’é:
Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal.
Traduxi da-o ligure à l’ingleise:
O fæto che o GCD o pòsse vegnî delongo espresso à sta mainea o se conosce comme identitæ de Bézout.
A traduçion in ingleise do testo a l’é:
The fact that the GCD can always be expressed in this way is known as Bézout's identity.
Quæ a l’é a traduçion ingleise de sto testo?
Con sta megoria, l’algoritmo o domanda nint’atro che çinque vòtte a quantitæ de giffre (à base 10) de l’intrego ciù piccin.
A traduçion in ingleise do testo a l’é:
With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer.
Traduxi in lengua ingleise:
L’algoritmo d’Euclide o l’à ben ben d’applicaçion, tanto teòriche comme prattiche.
A traduçion in ingleise do testo a l’é:
The Euclidean algorithm has many theoretical and practical applications.
Traduxi sto testo da-o zeneise à l’ingleise:
L’algoritmo d’Euclide o peu ëse deuviou pe resòlve de equaçioin diofantiñe, pe exempio pe attrovâ di numeri che satisfan de cogruense multiple segondo o teoremo do resto cineise, pe construe de fraçioin continuæ e pe attrovâ d’approscimaçioin raçionale accuræ pe-i numeri reali.
A traduçion in ingleise do testo a l’é:
The Euclidean algorithm may be used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers.
Comm’à l’é a traduçion ingleise de sto testo?
O mascimo divisô commun o ven scrito de spesso comme gcd(a, b) ò, con ciù sempliçitæ, comme (a, b), sciben che quest’urtima a l’é ciù ambigua e deuviâ ascì pe di atri conçetti, comme un ideale inte l’anelli di numeri intreghi, ligou à curto fî co-o MDC.
A traduçion in ingleise do testo a l’é:
The greatest common divisor is often written as gcd(a, b) or, more simply, as (a, b), although the latter notation is ambiguous, also used for concepts such as an ideal in the ring of integers, which is closely related to GCD.
Traduxi sto testo da-o zeneise à l’ingleise:
Pe fâ un exempio, ni o 6 e ni o 35 en di numeri primmi, da-o momento che tutti doî an doî fattoî primmi: 6 = 2 × 3 e 35 = 5 × 7.
A traduçion in ingleise do testo a l’é:
For example, neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2 × 3 and 35 = 5 × 7.
Traduxi da-o ligure à l’ingleise:
A fattorizzaçion de numeri intreghi erti a l’é tegnua pe un problema be ben complesso da-o ponto de vista computaçionâ, e e a seguessa de tanti protocòlli criptografichi deuviæ in sce larga scâ a l’é basâ in sciâ seu inattuabilitæ.
A traduçion in ingleise do testo a l’é:
Factorization of large integers is believed to be a computationally very difficult problem, and the security of many widely used cryptographic protocols is based upon its infeasibility.
Traduxi sto testo da-o zeneise à l’ingleise:
L’insemme de tutte e combinaçioin lineare integrale de a e b o l’é, in realtæ, o mæximo che l’insemme de tutti i moltipli de g (mg, donde m o l’é un intrego).
A traduçion in ingleise do testo a l’é:
The set of all integral linear combinations of a and b is actually the same as the set of all multiples of g (mg, where m is an integer).
Traduxi sto testo da-o zeneise à l’ingleise:
Dita à un atro mòddo, i moltipli do numero ciù piccin rk-1 vëgnan sottræti da quello ciù grande rk-2 fintanto che o resto rk o l’é ciù piccin de rk-1.
A traduçion in ingleise do testo a l’é:
In other words, multiples of the smaller number rk−1 are subtracted from the larger number rk−2 until the remainder rk is smaller than rk−1.
Traduxi sto testo in ingleise:
Coscì, c o dividde l’arregòrdo r0, dæto a-o comenso, da-o momento che r0 = a − q0b = mc − q0nc = (m − q0n)c.
A traduçion in ingleise do testo a l’é:
Therefore, c divides the initial remainder r0, since r0 = a − q0b = mc − q0nc = (m − q0n)c.
Traduxi sto testo da-o ligure à l’ingleise:
Pe primma cösa çerchemmo de impî o rettangolo con di quaddri b-by-b; à tutti i mòddi, à sta mainea o rettangolo r0-by-b (donde r0 < b) o l’arresta descoverto. Dapeu çerchemmo de impî o rettangolo ch’o l’arresta con di quaddri r0-by-r0.
A traduçion in ingleise do testo a l’é:
We first attempt to tile the rectangle using b-by-b square tiles; however, this leaves an r0-by-b residual rectangle untiled, where r0 < b. We then attempt to tile the residual rectangle with r0-by-r0 square tiles.
Traduxi da-o zeneise à l’ingleise:
O teorema a-a base da definiçion da divixon euclidea o l’assegua che quello quoçiente e o resto existan e son delongo unichi.
A traduçion in ingleise do testo a l’é:
The theorem which underlies the definition of the Euclidean division ensures that such a quotient and remainder always exist and are unique.
Quæ a l’é a traduçion ingleise de sto testo?
A-a fin de l’iteraçion do çiclo, a variabile b a tëgne o resto rk, mentre a variabile a a tëgne o seu predeçessô, rk-1.
A traduçion in ingleise do testo a l’é:
At the end of the loop iteration, the variable b holds the remainder rk, whereas the variable a holds its predecessor, rk−1.
Ti peu tradue sto testo in ingleise?
O matematico e stòrico B. L. van der Waerden o suggerisce che o Libbro VII o derive da un libbro de testo in sciâ teoria di numeri scrito da di studioxi de matematica da scheua de Pitagora.
A traduçion in ingleise do testo a l’é:
The mathematician and historian B. L. van der Waerden suggests that Book VII derives from a textbook on number theory written by mathematicians in the school of Pythagoras.
Traduxi in ingleise:
De çentanæa d’anni apreuvo, l’algoritmo d’Euclide o l’é stæto descoverto independentemente tanto inte l’India comme inta Ciña, ciù che tutto pe risòlve e equaçioin diofantiñe che nasceivan inte l’astronomia e inta realizzaçion de lunäi esatti.
A traduçion in ingleise do testo a l’é:
Centuries later, Euclid's algorithm was discovered independently both in India and in China, primarily to solve Diophantine equations that arose in astronomy and making accurate calendars.
Traduxi in lengua ingleise:
Do secolo XIX l’algoritmo euclideo o l’à portou a-o sviluppo de neuvi scistemi de numeraçion, comme i intreghi gaussien e intreghi de Eisenstein.
A traduçion in ingleise do testo a l’é:
In the 19th century, the Euclidean algorithm led to the development of new number systems, such as Gaussian integers and Eisenstein integers.
Quæ a l’é a traduçion ingleise de sto testo?
Pâ che Peter Gustav Lejeune Dirichlet o segge stæto o primmo à descrive l’algoritmo euclideo comme a base de gran parte da teoria di numeri.
A traduçion in ingleise do testo a l’é:
Peter Gustav Lejeune Dirichlet seems to have been the first to describe the Euclidean algorithm as the basis for much of number theory.
Ti peu tradue sto testo in ingleise?
Pe fâ un exempio, Dedekind o l’é stæto o primmo à demostrâ o teorema di doî quaddræ de Fermat pe mezo da fattorizzaçion unica di intreghi gaussien.
A traduçion in ingleise do testo a l’é:
For example, Dedekind was the first to prove Fermat's two-square theorem using the unique factorization of Gaussian integers.