Question

Arătați că (5n+ 4 , 6n+ 5) = 1 ajutor dau coroana repedeeeee

Answer 1

$\displaystyle\it\\notam~d=(5n+4,~6n+5),~atunci:\\d|5n+4,~atunci~d~va~divide~si~pe~6(5n+4).\\d|6n+5~atunci~d~va~divide~si~pe~5(6n+5).\\evident,~d~va~divide~si~diferenta~celor~doua~numere:\\d|5(6n+5)-6(5n+4)=30n+25-30n-24=\boxed{1} \implies d|1 \implies\\\boxed{\it d=1}.\\\\prin~urmare,~\boxed{\it (5n+4,6n+5)=1}.$