Докажите, что (5*4^6-40) кратно 70. Created by genakoshak2014. algebra-ru

Докажите, что (5*4^6-40) кратно 70...

ВладимирБ

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Решение смотри на фото

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ВикаВикторовна

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5*4⁶-40 = 5*(2²)⁶-5*8 = 5*2¹²-5*2³ = 5*2³(2⁹-1) = 5*2³((2³)³-1³) = 5*2³(2³-1)((2³)²+2³+1) = 5*2³(8-1)(2⁶+2³+1) = 5*2*2²*7(2⁶+2³+1) = 70*2²(2⁶+2³+1)
70*2²(2⁶+2³+1) : 70 = 2²(2⁶+2³+1)

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