Question

Va rog mult !!!

Demonstrati ca!! va rog urgentt

$2 ^{n} + 3 {}^{n} |4 {}^{n} + 6 {}^{n} \\ \\ \\ \\ 9 {}^{n} - 3 {}^{n} |3 {}^{n} - 1$
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Answer 1

Explicație pas cu pas:

${4}^{n} + {6}^{n} = {(2 \cdot 2)}^{n} + {(2 \cdot 3)}^{n} = {2}^{n} \cdot {2}^{n} + {2}^{n} \cdot {3}^{n} =$

$= {2}^{n} \cdot ({2}^{n} + {3}^{n}) \ \ \vdots \ \ {2}^{n} + {3}^{n}$

$\implies 2^{n} + {3}^{n} \ \Big| \ {4}^{n} + {6}^{n}$

.

${9}^{n} - {3}^{n} = {(3 \cdot 3)}^{n} - {3}^{n} = {3}^{n} \cdot ({3}^{n} - 1)$

$\implies {9}^{n} - {3}^{n} \ \nmid \ {3}^{n} - 1$

dar este adevărată afirmația:

$\implies {9}^{n} - {3}^{n} \ \ \vdots \ \ {3}^{n} - 1$

sau:

$\implies {3}^{n} - 1 \ \Big| \ {9}^{n} - {3}^{n}$