Question

DAU COROANĂ!!!
E urgent!
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Answer 1

Explicație pas cu pas:

b)

$\overline {5x4y} \ \ \vdots \ \ 12, \ 12 = 3 \cdot 4, \ (3,4) = 1 \\ \implies \overline {5x4y} \ \ \vdots \ \ 3 \ \ si \ \ \overline {5x4y} \ \ \vdots \ \ 4$

$\overline {5x4y} \ \ \vdots \ \ 4 \implies y \in \{0; 4; 8\}$

$\overline {5x4y} \ \ \vdots \ \ 3 \iff (5+x+4+y) \ \ \vdots \ \ 3 \\ \iff (x+y+9) \ \ \vdots \ \ 3 \implies (x+y) \ \ \vdots \ \ 3$

$y = 0 \implies (x+0) \ \ \vdots \ \ 3 \iff x \ \ \vdots \ \ 3 \implies x \in \{0; 3; 6; 9\} \\ \implies \bf 5040, 5340, 5640, 5940$

$y = 4 \implies (x+4) \ \ \vdots \ \ 3 \implies x \in \{2; 5; 8\} \\ \implies \bf 5244, 5544, 5844$

$y = 8 \implies (x+8) \ \ \vdots \ \ 3 \implies x \in \{1; 4; 7\} \\ \implies \bf 5148, 5448, 5748$

c)

$\overline {3a4b} \ \ \vdots \ \ 45, \ 45 = 5 \cdot 9, \ (5,9) = 1 \\ \implies \overline {3a4b} \ \ \vdots \ \ 5 \ \ si \ \ \overline {3a4b} \ \ \vdots \ \ 9$

$\overline {3a4b} \ \ \vdots \ \ 5 \implies b \in \{0; 5\}$

$\overline {3a4b} \ \ \vdots \ \ 9 \iff (3+a+4+b) \ \ \vdots \ \ 9 \\ \iff (a+b+7) \ \ \vdots \ \ 9$

$b = 0 \implies (a+7) \ \ \vdots \ \ 9 \implies a = 2 \implies \bf 3240$

$b = 5 \implies (a+12) \ \ \vdots \ \ 9 \implies a = 6 \implies \bf 3645$