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asatbeksultanov
@asatbeksultanov
June 2022
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Доказать,что число 5^8-3^4 и делиться на 11
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koingrel
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5^8 - 3^4 = (5^4 - 3^2)(5^4 + 3^2) = (5^2 - 3)(5^2 + 3^2)(5^4 + 3^2) = 22*(5^2 + 3^2)(5^4 + 3^2) = 11*2*(5^2 + 3^2)(5^4 + 3^2) => число 5^8-3^4 делится на 11.
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5^8 - 3^4 = (5^4 - 3^2)(5^4 + 3^2) = (5^2 - 3)(5^2 + 3^2)(5^4 + 3^2) = 22*(5^2 + 3^2)(5^4 + 3^2) = 11*2*(5^2 + 3^2)(5^4 + 3^2) => число 5^8-3^4 делится на 11.