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Консультация № 187200
12.03.2013, 20:29
137.06 руб.
13.03.2013, 08:10
0
4
3
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Доброго времени, не совсем уверен, что пишу в правильный раздел.
хочу проверить правильность своего решения по предмету надежность систем.
задача:
найти значение "В" в выражении В*А (mod N)=1 при А=5, N=8
Доброго времени, не совсем уверен, что пишу в правильный раздел.
хочу проверить правильность своего решения по предмету надежность систем.
задача:
найти значение "В" в выражении В*А (mod N)=1 при А=5, N=8
Обсуждение
12.03.2013, 23:01
общий
это ответ
Здравствуйте, Матвеев Денис Александрович!
При заданных значениях параметров выражение принимает вид 5В (mod 8)=1
a=b (mod n) равносильно тому, что остатки от деления a и b на n одинаковы;
То есть остатки от деления 5В и 1 на 8 одинаковы.
Следовательно, остаток от деления 5В на 8 равен 1.
5B=8k+1, k - целое
B=1,6k+0,2
При заданных значениях параметров выражение принимает вид 5В (mod 8)=1
a=b (mod n) равносильно тому, что остатки от деления a и b на n одинаковы;
То есть остатки от деления 5В и 1 на 8 одинаковы.
Следовательно, остаток от деления 5В на 8 равен 1.
5B=8k+1, k - целое
B=1,6k+0,2
12.03.2013, 23:03
общий
это ответ
Здравствуйте, Матвеев Денис Александрович!
B может принимать множество значений, минимальное - 5, потому что 25 mod 8=1
B может принимать множество значений, минимальное - 5, потому что 25 mod 8=1
13.03.2013, 08:08
общий
это ответ
Здравствуйте, Денис Александрович!
Если подставить в общее выражение числовые значения, получим 1 [$8801$] 5B (mod 8). Это значит, что числам 1 и 5B при делении на 8 соответствует один и тот же остаток.
Используя свойства сравнений, получим, что
- сравнение с одним неизвестным, которое имеет столько решений, сколько вычетов полной системы ему удовлетворяет.
Сравнению (1) среди чисел 0, 1, 2, 3, 4, 5, 6, 7 полной системы вычетов по модулю 8 удовлетворяет только число B = 5. К этому классу решений относятся и все числа, сравнимые с числом 5 по модулю 8, например, числа -11, -3, 13 и т. д.
С уважением.
Если подставить в общее выражение числовые значения, получим 1 [$8801$] 5B (mod 8). Это значит, что числам 1 и 5B при делении на 8 соответствует один и тот же остаток.
Используя свойства сравнений, получим, что
5B - 1 [$8801$] 0 (mod 8) (1)
- сравнение с одним неизвестным, которое имеет столько решений, сколько вычетов полной системы ему удовлетворяет.
Сравнению (1) среди чисел 0, 1, 2, 3, 4, 5, 6, 7 полной системы вычетов по модулю 8 удовлетворяет только число B = 5. К этому классу решений относятся и все числа, сравнимые с числом 5 по модулю 8, например, числа -11, -3, 13 и т. д.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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