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Консультация № 189360
13.05.2016, 20:40
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
сколько существует решений уравнения х1+х2+...+х80=20 в целых числах, где хi>=-1?
сколько существует решений уравнения х1+х2+...+х80=20 в целых числах, где хi>=-1?
Обсуждение
14.05.2016, 07:54
общий
это ответ
Здравствуйте, Александр!
Если сделать замены переменных по формуле
то задача сведётся к нахождению количества решений в целых числах уравнения 
где 
Насколько мне известно, количество решений в целых числах уравнения вида 
где 
ищется исходя из того, что поставленная задача аналогична задаче о количестве различных выборок вида 
где имеется 
объектов типа 
и 
Для этого используется формула количества сочетаний с повторениями из 
элементов по 
элементов:
В нашем случае
что после подстановки в формулу (1) даёт
различных решений заданного уравнения.
Литература
Андерсон Д. Дискретная математика и комбинаторика. : Пер. с англ. - М. : Издательский дом "Вильямс", 2004. - 960 с.
С уважением.
Если сделать замены переменных по формуле
то задача сведётся к нахождению количества решений в целых числах уравнения где Насколько мне известно, количество решений в целых числах уравнения вида где ищется исходя из того, что поставленная задача аналогична задаче о количестве различных выборок вида где имеется объектов типа и Для этого используется формула количества сочетаний с повторениями из элементов по элементов:В нашем случае
что после подстановки в формулу (1) даётразличных решений заданного уравнения.
Литература
Андерсон Д. Дискретная математика и комбинаторика. : Пер. с англ. - М. : Издательский дом "Вильямс", 2004. - 960 с.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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