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Консультация № 190716
16.03.2017, 17:46
0.00 руб.
16.03.2017, 20:35
1
2
1
Здравствуйте! У меня возникли сложности с таким вопросом (в приложении):
Назовём два натуральных числа "почти соседними", если каждое из них делится (без остатка) на их разность. На уроке математики Андрея попросили выписать в тетрадь все числа, почти соседние с числом 2533. Сколько чисел придётся выписать Андрею?
Назовём два натуральных числа "почти соседними", если каждое из них делится (без остатка) на их разность. На уроке математики Андрея попросили выписать в тетрадь все числа, почти соседние с числом 2533. Сколько чисел придётся выписать Андрею?
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Обсуждение
16.03.2017, 20:34
общий
это ответ
Здравствуйте, svrvsvrv!
Натуральными делителями числа
являются только степени двойки от 
до 
Следовательно, почти соседними с этим числом могут быть только следующие числа, разности которых с числом содержат в своих канонических разложениях эти степени:
(всего 
числа);
(всего 
числа).
Понятно, что наибольшим числом является
разность 
является делителем числа 
и наибольшим делителем числа Аналогично, наименьшим числом является 
Итого
чисел придётся выписать Андрею, если я правильно посчитал. 
Натуральными делителями числа
являются только степени двойки от до Следовательно, почти соседними с этим числом могут быть только следующие числа, разности которых с числом содержат в своих канонических разложениях эти степени: (всего числа); (всего числа).Понятно, что наибольшим числом является
разность является делителем числа и наибольшим делителем числа Аналогично, наименьшим числом является Итого
чисел придётся выписать Андрею, если я правильно посчитал.
5
Спасибо.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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