[tex]\displaystyle\bf\\Notam~(2k+1,~9k+4)=d,~unde~d~este~cel~mai~mare~divizor~comun\\al~celor~doua~numere.\\In~mod~evident,~d|(2k+1),~iar~d|(9k+4),~atunci~d~va~divide~si~pe\\9(2k+1),~respectiv~pe~2(9k+4),~deci,~d|(18k+9),~iar~d|(18k+8),~\\atunci~d~va~divide~si~diferenta~celor~doua~numere,\\~d|[(18k+9)-(18k+8)],~deci~d|1\implies\boxed{\bf d=1}.[/tex]
