Question

$aratati \: ca \: b = 2 {}^{0} + 2 {}^{1} + 2 {}^{2} + 2{}^{3} + 2 {}^{4} + 2 {}^{5} + 2 {}^{6} + ... + 2 {}^{2003} se \: divide \: cu \: 15$
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Answer 1

Explicație pas cu pas:

$b = {2}^{0} + {2}^{1} + {2}^{2} + {2}^{3} + {2}^{4} + {2}^{5} + {2}^{6} + ... + {2}^{2003} = ( {2}^{0} + {2}^{1} + {2}^{2} + {2}^{3} ) + {2}^{4} \times ( {2}^{0} + {2}^{1} + {2}^{2} + {2}^{3} ) + ... + {2}^{2000} \times ( {2}^{0} + {2}^{1} + {2}^{2} + {2}^{3} ) = (1 + 2 + 4 + 8) + {2}^{4} \times (1 + 2 + 4 + 8) + {2}^{2000} \times (1 + 2 + 4 + 8) = 15 \times (1 + {2}^{4} + ... + {2}^{2000} )se \: divide \: 15$

Mult succes în continuare!