Question

Suma elementelor multimii M={x|x apartine N, 18 divide x si x-1 divide 5} este egala cu.......

Answer 1

$M = \Big\{ x \big| x\in \mathbb_{N} , 18 \vdots x, si (x-1) \vdots 5 \Big\} \\ \\ \boxed{1} \quad 18 \vdots x \Rightarrow x\in D_{18}^+\Rightarrow x\in \Big\{1,2,3,6,9,18\Big\} \\ \\ \boxed{2} \quad (x- 1) \vdots 5 \Rightarrow x - 1 = 5k \Rightarrow x = 5k+1,\quad k\in \mathbb_{Z^+} \Rightarrow \\ \\ \Rightarrow x \in\Big\{5\cdot 1+1, 5\cdot 2+1, 5\cdot 3+1, 5\cdot 4+1,...\Big\} \Rightarrow x \in\Big\{6,11, 16,21,...\Big\}$

$\ Din \boxed{1} \cap \boxed{2} \Rightarrow x \in \big\{6\big\} \Rightarrow M = \big\{6\big\} \Rightarrow \boxed{S = 6}$