L'algorisme d'Euclides ampliat o algorisme d'Euclides estès és una millora de l'algorisme d'Euclides de càlcul del màxim comú divisor de dos nombres enters, que dona, a més del màxim comú divisor dels dos nombres, els coeficients de cadascun d'aquests dos nombres a la identitat de Bézout.
Siguin
i
dos nombres enters. L'algorisme d'Euclides consisteix a construir la recurrència finita
en la qual
no és més que el residu de la divisió entera de
i
amb quocient
. La successió és estrictament decreixent i la condició
obliga a que sigui finita. L'últim terme, posem
arriba quan hi ha
que fa
. La successió té, doncs,
termes i
.
Però si ara considerem aquestes altres dues recurrències finites:
amb els valors
de la successió de l'algorisme d'Euclides, resulta que, per
amb
, es té
com es comprova fàcilment per inducció.
Per tant, si
, resulta
i
i
, amb els signes adequats, són els coeficients de
i
a la identitat de Bézout.
Hom sol disposar els càlculs en una graella com aquesta
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle x_{3}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO83zDnCajBFzjC4zDC5oAsPagsOzNnFnjw5atw1oNCOaqo4o2dBaNa1) |
![{\displaystyle x_{4}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9AoDGOyjK2zAs4aAs0yto2zDnEatK5nAo3agw4ntdAnje0otK5ntrA) |
![{\displaystyle x_{5}\ldots \ldots x_{i-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Byjo3aAaPzgrDngs0ytdDnAiNoDG5nDi2yjaNatdEyjrEytm0ytnE) |
![{\displaystyle x_{i-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9CoDa0zqdEzDJEnji0ajw3zjK0aAnFnDrCaAnAnDaPzgvFotm0ntaN) |
![{\displaystyle x_{i}\ldots \ldots x_{k-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9BzAwNyga3zqi3oAa1ajK3ntC5yjsPajlEytGOajwOaDvCzgzEz2wQ) |
![{\displaystyle x_{k-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85oNoQoNw0zjaPajKPytG5yjzEaqzBnjC4ygaNzgeOaNFEo2w5ati5) |
|
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle y_{3}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80ntKNotCQatm0otBEzDw4zgi2oAaOngoNzqrCnDw2yqw2aNm3oDdD) |
![{\displaystyle y_{4}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO82yjs5ntCQajzCytm2ntoOzArCoNK3aDi1ngw2otBFyjC2nAiNoDhB) |
![{\displaystyle y_{5}\ldots \ldots y_{i-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8PaDBEaDK4zNC4otsOa2vFotK0oNCOa2zCzAzBnjzDaqi3aDeOzgsP) |
![{\displaystyle y_{i-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8Najs2agw3yjKPoNmNage5zjmNyqoQoqo4yqdCaDKNztrCajwPaNzC) |
![{\displaystyle y_{i}\ldots \ldots y_{k-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8PnDG5aDwOzqhAaqvCztJBzDnCntKPztw2ntmOz2a1aqzDatzCotFB) |
![{\displaystyle y_{k-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO84zgzCoNGNote4aDw5zNC0otJDzji1aDi4zDm1yqe2oAi5zta0ztrC) |
|
|
![{\displaystyle q_{3}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9DatG4zNiPnAnDntoQz2a4ngw3ztm0otnCo2e1aDi5zAs4oDo3age4) |
![{\displaystyle q_{4}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EzgoOaNwOnjKNnjKOatzBoDBDzjJCoDoOnDJBoNaPatKOnjrDoNwN) |
![{\displaystyle q_{5}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8Oztw3atm2a2wNaDC1aAdCyje3ajC5z2rCoNlCago4oqzEzDaQaAnC) |
![{\displaystyle q_{6}\ldots \ldots q_{i-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80yjzAngi2oqo1yjvCnAe2aqdFnqa2yqhEzNJAztsNzqsOzjKOatoO) |
![{\displaystyle q_{i}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OzNsOngzEnAo4yjwNztwQzDBAntaNaAe4ntsPnqeQotKQotsNaqe2) |
![{\displaystyle q_{i+1}\ldots \ldots q_{k-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO84oDK3aqa5nArEoDi3oNBAytrEntrEaji5a2iNaji0zga2zDC1zAe4) |
![{\displaystyle q_{k}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9AaDKOatrBzjnFoAzFnjoQnDiQajwNzgwOoNGQajaNatm1yjlFnDC1) |
|
![{\displaystyle |a|}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO84oDoPnjrEoqiQztmQzjGPzqoNoqdDztdAzti3o2s2aAe2ajBEyqe2) |
![{\displaystyle |b|}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO84yjhAzjBBytwNyjFFzjnFajrCaNe5aDsPztsPo2sOagdFnDvAajrC) |
![{\displaystyle d_{3}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8QnDm1aqdCatdEztwPaNmPzgrBoDw5zjw4atnDoDs2zNdBngnDnAo0) |
![{\displaystyle d_{4}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9CzjzByjnByje4oNo4zNhCatlFzNlBzga4zAi2o2rFaDwPztC5aqoQ) |
![{\displaystyle d_{5}\ldots \ldots d_{i-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9FyjvEyjiQzts4oAw3oDrAzjCOzNe3aqaPnjKNaNC2nja0agePaAo2) |
![{\displaystyle d_{i-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80aDvBaDhFoDlAyga3nAhDotdEotK5zqrEa2hCz2a0nDeOzjJFytFC) |
![{\displaystyle d_{i}\ldots \ldots d_{k-2}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoDmOaqe0zDK2yji1ajs4zNeNzqs1otwOztsNotwPz2hEaqnAo2iN) |
![{\displaystyle d_{k-1}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO83zgs3aDo5yjaPzjiOytzEytwQzNG1yjzFo2dEzNw0ajGPzqi0oNFE) |
![{\displaystyle d_{k}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EzNFAzqeOoqdDzjFBzDzEytG3oDnCzNsOz2zFotrFotBEaqdEztiO) |
|
Hom comença obtenint
com a quocient de la divisió entera de
entre
, és a dir,
entre
i
a partir de
. Els termes
i
resulten de
i
. Els termes següents,
,
,
i
s'obtenen de la mateixa manera i en el mateix ordre:
i el procés acaba quan trobem
. Aleshores,
Il·lustrem aquest procés amb un exemple: es tracta de calcular
:
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle -2}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80zAs1oDrEzjoOnts0zAePnjzCz2s1nDBFaDzBnArDntwQzqeOntK4) |
![{\displaystyle 3}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85ythBaNzDzAsOajJEate1zjnAatrEngnBntFEztKOzArFnAdEoDdA) |
|
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle -4}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9FngvDyjsPytKOzgo4aqe0a2i2yjGNoNrBoDdDytC2nDBAoNe5ytnA) |
![{\displaystyle 9}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8NaAwNnjhBaqo5ngnBaje1zga2aDGNzNBBzDBFzDC3athAntvBoqdC) |
![{\displaystyle -13}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80zta1otlCzjw3yqrCaArCzjeOygw2aqnFajoNaNoNz2a1aDrFotC4) |
|
|
![{\displaystyle 4}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OytrEzgdAaqvBz2zCaNsQags3zjlBago0nDm2aNrCoDeOnjG3oDwO) |
![{\displaystyle 2}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85ajhAoNCPagaPytC5agwQngdFoqrAntw3aDnDnqePotvBaDi3otlA) |
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle 3}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85ythBaNzDzAsOajJEate1zjnAatrEngnBntFEztKOzArFnAdEoDdA) |
![{\displaystyle 2}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85ajhAoNCPagaPytC5agwQngdFoqrAntw3aDnDnqePotvBaDi3otlA) |
|
![{\displaystyle 763}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Doqw0ntzEntK5yjsNntm2oqrEotvFyjvEaAzBaAeOngwPaAe0oDi4) |
![{\displaystyle 175}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9AzNwQzAdBz2zBo2vEygnDnAnAnDsOatGQygrCaDKQz2dBoAvFytFB) |
![{\displaystyle 63}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Bzqs2yjKQythEoDw5yjzEotnDntFDngo5ajFCzNK4oAhBnAnEo2dF) |
![{\displaystyle 49}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO80ntG1zghCoDzCaNC3zDdEzjrFnqi5ntlEzgvAzti4yjiOz2a3otK0) |
![{\displaystyle 14}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8QztC5oNnCzqsPyjw4zDs5atlAzNK3njK0yts3ajaOzNiNnqrCztJB) |
![{\displaystyle 7}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9BntKPzArDzDiNyjdFzAe3ytsQytdDagrCnjG1yqwPaAs2zgzEoAi4) |
|
que prové de
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle 1=1-4\cdot 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO82njsNytrEnDo3ntC0nArAyto1nDvDyjGQa2o5yqw5ytzCaje1agdD) |
![{\displaystyle -2=0-2\cdot 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EnArDytC0nAs0a2vAnAs1nDlEotlByjiPaNK1oqwPzNlEatoNnDlE) |
![{\displaystyle 3=1-1\cdot (-2)}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9BzDoQzDw1ztmNnAdCaqe1aDo3atwQztG3zjG4oDeQngvDzAw0yjzA) |
|
![{\displaystyle 0}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8OoqhByjG2zgiNoNhAnqa5ztG1aDoPzNCPotGQyqvCnqaPzjG5ytsQ) |
![{\displaystyle 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO85aAw5yge4aAiNzNK4nDm0aNiQygw0nteQytoQotCPytzCnDs3o2dA) |
![{\displaystyle -4=0-4\cdot 1}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EajdBzgnFoqnAateOz2oQz2dCnjw5aqdDnjFDzjm2aAi0o2o2nts3) |
![{\displaystyle 9=1-2\cdot (-4)}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EnqePatoNztBFzNeNaga1o2a0zNK2aAw5aAi4ntKQzqvBzjGOa2a0) |
![{\displaystyle -13=-4-1\cdot 9}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9FzgvBz2sNzqaOote0atKOaAs2aDaPzgdDatKNz2rEo2hEa2nCo2w0) |
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|
![{\displaystyle 4=763\div 175}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO82zDmNnDBBztGPaNzCotlDnti5aDiOoqvBajm0aNKPaAa5zqo1oqs3) |
![{\displaystyle 2=175\div 63}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9CyjC0njCOnDKQzDnBotzEzAe0zjm1o2vAnAa3zNhCzghCatwQyqs3) |
![{\displaystyle 1=63\div 49}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8QzDhBo2s2oNaPygo2aNi2ygo1ygs3aNo3oNnCytiQaAiPagePzAhF) |
![{\displaystyle 3=49\div 14}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO81zDKNoDeNyjw2ygvCytmNaNlEzAo0ajrAoNwNaAoPoNBBnga2zqa2) |
![{\displaystyle 2=14\div 7}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9BnAi3ygs2ztFCyqe5ztsNnDmNaDo2atJBytw5zAvAnqa2oAa1zNlC) |
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![{\displaystyle 763}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Doqw0ntzEntK5yjsNntm2oqrEotvFyjvEaAzBaAeOngwPaAe0oDi4) |
![{\displaystyle 175}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9AzNwQzAdBz2zBo2vEygnDnAnAnDsOatGQygrCaDKQz2dBoAvFytFB) |
![{\displaystyle 63=763-175\cdot 4}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9CyjGQnAnEataNoNrCnqw5zAaOoNnFnDo1a2w5aDlBota5ygzCnja2) |
![{\displaystyle 49=175-63\cdot 2}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO83oNi5a2wQaDhCzDGNnjhCyjC1zNvEo2sQzNi2aDKQoNw2aDs5aAwO) |
![{\displaystyle 14=63-1\cdot 49}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9CztnFytK4yjs1otmNa2w4otK2zjo1zDrAngdAytiPaNa2zthFoqvA) |
![{\displaystyle 7=49-3\cdot 14}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8Qzgs5aAi4atzFzjeOytiOotCNaNvFa2o2nts4aNs4z2ePoDKQotvB) |
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(Les divisions
se sobreentenen enteres) Aleshores,
.