Деление на 37

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Сложность: 

Трёхзначное число ABC делится на 37. Докажите, что сумма чисел BCA и CAB тоже делится на 37.

Решение

Поскольку

ABC + BCA + CAB = 111 × (A + B + C) = 3 × 37 × (A + B + C)

делится на 37, и первое слагаемое тоже делится на 37, то и сумма двух других слагаемых должна делиться на 37.




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