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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос 1-Решить диофантово уравнение 2314х-4121у=26 2- представить число корень из 119 в виде периодической цепной дроби и приблизить его подходящей дробью с точностью 10 в -4 степени 3-найти наименьшее натуральное х удовлетворяющее соотношениям х=9(mod 11)x= 1(mod 13) x=4(mod 9) 6 вариант в файле
Решим сначала уравнение используя алгоритм Евклида (числа и -- взаимно простые, поэтому их наибольший общий делитель равен единице):
Отсюда получим, что
То есть
Значит, частным решением уравнения являются числа и Проверим полученное частное решение подстановкой чисел и в левую часть заданного уравнения. Получим как и должно быть.
Определим вид общего решения заданного диофантова уравнения. Для этого из уравнения вычтем равенство Получим уравнение Тогда откуда видно, что число будет целым тогда и только тогда, когда число делится на то есть где -- целое число. Следовательно, общее решение заданного диофантова уравнения имеет вид
где -- целое число.
Об авторе:
Facta loquuntur.
Форма ответа
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Timur 
используя алгоритм Евклида (числа 
и 
-- взаимно простые, поэтому их наибольший общий делитель равен единице):
являются числа 
и 
Проверим полученное частное решение подстановкой чисел 
и 
в левую часть заданного уравнения. Получим 
как и должно быть.
Получим уравнение 
Тогда 
откуда видно, что число 
будет целым тогда и только тогда, когда число 
делится на 
то есть 
где 
-- целое число. Следовательно, общее решение заданного диофантова уравнения имеет вид
где