Question

Determinați elementele mulțimii A {x €N| 63/2x+1€N}

Answer 1

$A=\left\{x\:\in\:\mathbb{N}\:|\:\frac{63}{2x+1}\:\in\:\mathbb{N}\right\}$

$\frac{63}{2x + 1} \:\in\:\mathbb{N} = >2x + 1 \: \in \: D_{63_{+}}$

$D_{63_{+}}=\left\{1,3,7,9,21,63\right\}$

$1)2x + 1 = 1$

$2x = 1 - 1$

$2x = 0$

$x = 0 \: \in \: \mathbb{N}$

$2)2x + 1 = 3$

$2x = 3 - 1$

$2x = 2 \: | \div 2$

$x = 1 \: \in \: \mathbb{N}$

$3)2x + 1 = 7$

$2x = 7 - 1$

$2x = 6 \: | \div 2$

$x = 3 \: \in\: \mathbb{N}$

$4)2x + 1 = 9$

$2x = 9 - 1$

$2x = 8 \: | \div 2$

$x= 4 \: \in \: \mathbb{N}$

$5)2x + 1 = 21$

$2x = 21 - 1$

$2x = 20 \: | \div 2$

$x = 10 \: \in \: \mathbb{N}$

$6)2x + 1 = 63$

$2x = 63 - 1$

$2x = 62 \: | \div 2$

$x = 31 \: \in \: \mathbb{N}$

$= > x \: \in \: \left\{0,1,3,4,10,31\right\}$

$= > A=\left\{0,1,3,4,10,31\right\}$