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Консультация № 182803
11.04.2011, 17:40
0.00 руб.
0
7
1
Здравствуйте! Прошу помощи в следующем вопросе:
Найдите целое решение выражения:
Найдите целое решение выражения:
Обсуждение
11.04.2011, 18:05
общий
Здравствуйте!
Наверное, Вы имели в виду "целое решение уравнения"?
С уважением.
Наверное, Вы имели в виду "целое решение уравнения"?
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
11.04.2011, 18:32
общий
Адресаты:
Там откуда я брал задание написано выражение. Но даже с моими скудными познаниями в математике мне показалось, что это уравнение. Вот только спросить не у кого вот и написал как в оригинале. А что это так важно?
11.04.2011, 20:31
общий
это ответ
Здравствуйте, Protos!
Решение x = 0, y = 0 - единственное решение заданного уравнения. Доказать это можно так. Предположим, x > 0.
Положим
,
где z - целое число. Тогда имеем
Пусть
тогда
где p - натуральное число.
Имеем
а поскольку
то
что невозможно.
Ответ: {0, 0}.
Доказательство приведено по источнику
Базылев Д. Ф. Справочное пособие к решению задач: диофантовы уравнения. - Минск: НТЦ "АПИ", 1999. - 160 с.
С уважением.
Решение x = 0, y = 0 - единственное решение заданного уравнения. Доказать это можно так. Предположим, x > 0.
Положим
,где z - целое число. Тогда имеем
Пусть
тогда
где p - натуральное число.
Имеем
а поскольку
то
что невозможно.
Ответ: {0, 0}.
Доказательство приведено по источнику
Базылев Д. Ф. Справочное пособие к решению задач: диофантовы уравнения. - Минск: НТЦ "АПИ", 1999. - 160 с.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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