Предмет: Математика, автор: arslansevil1125

Докажите, что значение выражения: 46 ^ 3 + 4 ^ 3 делится на 50​

Ответы

Автор ответа: fumfumop1
0

Ответ:

Мы можем доказать это, используя отношение конгруэнтности в модульной арифметике.

Во-первых, мы можем переписать 46^3 как (50 - 4)^3:

(50 - 4)^3 = 50^3 - 3 * 50^2 * 4 + 3 * 50 * 4^2 - 4^3

Теперь, подставив значение 50^3, мы имеем:

50^3 - 3 * 50^2 * 4 + 3 * 50 * 4^2 - 4^3 = 125000 - 6000 + 600 - 64 = 119936

Итак, 46^3 + 4^3 = 119936 + 64 = 120000, что делится на 50.

Следовательно, выражение 46^3 + 4^3 делится на 50.

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