Question

Tìm n thuộc N biết

a, 2n + 19 chia hết cho 7

b, 5n + 1 chia hết cho 7

Answer 1

n+1\(⋮\)7 

\(\Rightarrow\)5n+1+14\(⋮7\)

\(\Rightarrow5n+15⋮7\)

\(\Rightarrow5(n+3)⋮7\)

\(\Rightarrow n+3⋮7\left(vi(5:7)=1\right)\)

\(\Rightarrow n+3\in B_{\left(7\right)}\)

\(\Rightarrow n+3=7k\left(k\inℕ^∗\right)\)

\(\Rightarrow n=7k-3\)

vậy n có dạng 7k-3

Answer 2

a, Ta có : 2n + 19 chia hết cho 7

\(\Rightarrow\) \(2n+19\inƯ\left(7\right)\)

Mà  \(Ư\left(7\right)=\left\{1;-1;7;-7\right\}\)

\(\Rightarrow\) \(2n+19\in\left\{1;-1;7;-7\right\}\)

\(\Rightarrow\) \(2n\in\left\{20;18;26;12\right\}\)

\(\Rightarrow\) \(n\in\left\{10;9;13;6\right\}\)

Answer 3

a.n=3

b.n=55