Question

Demonstrati ca daca 5| (3x+y), atunci 5| (2x-y), unde x, y∈Z.

Answer 1

$5~|~5 \Rightarrow 5~|~5(x+y) \Leftrightarrow 5~|~5x+5y. \\ \\ 5~|~5x+5y~si~5~|~3x+y \Rightarrow 5~|~(5x+5y)-(3x+y) \Leftrightarrow \\ \\ \Leftrightarrow \boxed{5~|~2x-y}~.$

Answer 2

5 I 5x+5y
iar 5I (5x+5y)-(3x+y)=2x-y