Предмет: Математика, автор: persik0808

Доведіть, що:
різниця чисел abc i cbа ділиться націло на 99.
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Ответы

Автор ответа: Medved23
3

\overline{abc}-\overline{cba}=(100a+10b+c)-(100c+10b+a)=99a-99c=99(a-c)

Поскольку 99⋮99, то 99(a-c) ⋮ 99. То есть (\overline{abc}-\overline{cba}) ⋮ 99, что и требовалось доказать.

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