При деление двух различных чисел на 3 в остатке 1 и 2 найдите остаток при выделении

При деление двух различных чисел на 3 в остатке 1 и 2 найдите остаток при выделении положительной разности квадратов
- Предмет:
  Математика
- Автор:
  nazariovmud
- 5 лет назад

Ответы 1

Пусть a имеет остаток 1, b имеет остаток 2, и a > b. Тогдаa = 3n+1; b = 3m+2a^2 - b^2 = (a - b)(a + b) = (3n+1-3m-2)(3n+1+3m+2) = (3n-3m-1)(3n+3m+3)Вторая скобка делится на 3, значит, и все число делится на 3.Если большее число имеет остаток 2, а меньшее остаток 1, то будет тоже самое.Ответ: разность квадратов этих чисел кратна 3.
- Автор:
  maximilian88
- 5 лет назад
- 0
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При деление двух различных чисел на 3 в остатке 1 и 2 найдите остаток при выделении положительной разности квадратов

Ответы 1

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