Question

Tìm số tự nhiên n để phân số A=21+3/6n+4

Answer 1

Gọi ƯCLN\((21n+3,6n+4)\)là d. Ta có :

\(\hept{\begin{cases}21n+3⋮d\\6n+4⋮d\end{cases}}\Rightarrow\hept{\begin{cases}126n+18⋮d\\126n+84⋮d\end{cases}}\)

\(\Rightarrow(126n+84)-(126n+18)⋮d\)

\(\Rightarrow66⋮d\)

\(\Rightarrow d\inƯ(66)\)

\(\Rightarrow21n+3⋮66\)

\(\Rightarrow21n+3-66⋮66\)

\(\Rightarrow21n-63⋮66\)

\(\Rightarrow21(n-3)⋮66\)

\(\Rightarrow n-3⋮66\)

\(\Rightarrow n-3=66k(k\inℕ)\)

\(\Rightarrow n=66k+3\)