Question

aratati ca fractia n supra 3n+1 este fractie ireductibila oricare ar fi n apartine nr naturale (N)

Answer 1

$\text{Fie~d~nr.~cu~care~simplificam~astfel~incat:}~ \\ d~|~n \\ ~si~ \\ d~|~3n+1(1). \\d~|~n/\cdot3\Rightarrow d~|~3n(2) \\\\Din~(1)~si~(2)\Rightarrow\text{d~divide~si~diferenta}\Rightarrow \\ d~|3n+1-3n\Rightarrow d~|~1\Rightarrow \boxed{d=1}\Rightarrow \text{Fractia~este~ireductibila.}$