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Консультация № 189063
01.04.2016, 20:01
0.00 руб.
02.04.2016, 06:54
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
как найти остаток от деления 31^(17^(37)) на 44?
как найти остаток от деления 31^(17^(37)) на 44?
Обсуждение
01.04.2016, 22:50
общий
это ответ
Здравствуйте, bill1091989!
Вычисляя остатки от деления на 44 степеней числа 31, можно заметить, что
последовательность остатков повторяется с периодом 10, т.е.
3110*n + k [$8801$] 31k (mod 44),
Аналогично, последовательность остатков от деления на 10 степеней числа 17 повторяется периодом 4:
174*n+k [$8801$] 17k (mod 10).
Поэтому 1737 [$8801$] 1737 - 4*9 [$8801$] 7 (mod 10).
Следовательно, 1737 = 10*n + 7.
3110*n + 7 [$8801$] 317 [$8801$] 15 (mod 44).
То есть, остаток от деления 31^(17^37) на 44 равен 15.
Вычисляя остатки от деления на 44 степеней числа 31, можно заметить, что
последовательность остатков повторяется с периодом 10, т.е.
3110*n + k [$8801$] 31k (mod 44),
Аналогично, последовательность остатков от деления на 10 степеней числа 17 повторяется периодом 4:
174*n+k [$8801$] 17k (mod 10).
Поэтому 1737 [$8801$] 1737 - 4*9 [$8801$] 7 (mod 10).
Следовательно, 1737 = 10*n + 7.
3110*n + 7 [$8801$] 317 [$8801$] 15 (mod 44).
То есть, остаток от деления 31^(17^37) на 44 равен 15.
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