Question

Determinati: numerele naturale de forma 8x1y5 divizibile cu 3 si cu 25

Answer 1

$\it \overline{8x1y5}\ \vdots\ 25\Rightarrow y\in\{2,7\} \\\\I)\ y=2 \Rightarrow \overline{8x125}\ \vdots\ 3 \Rightarrow (8+x+1+2+5)\ \vdots\ 3 \Rightarrow (16+x)\ \vdots\ 3 \Rightarrow x\in\{2, 5, 8\}\\\\II)\ y=7 \Rightarrow \overline{8x175}\ \vdots\ 3 \Rightarrow (8+x+1+7+5)\ \vdots\ 3 \Rightarrow (21+x)\ \vdots\ 3 \Rightarrow x\in\{0, 3, 6,9\}$

Numerele cerute sunt:

82125, 85125, 88125, 80175, 83175, 86175, 89175.