Question

Tìm số nguyên n sao cho (3n+24) chia hết (n-4)

Answer 1

\(\Leftrightarrow3n-12+36⋮n-4\)

\(\Leftrightarrow n-4\in\left\{1;-1;2;-2;3;-3;4;-4;6;-6;9;-9;12;-12;18;-18;36;-36\right\}\)

hay \(n\in\left\{5;3;6;2;7;1;8;0;10;-2;13;-5;16;-8;22;-14;40;-32\right\}\)

Answer 2

Ta có ; 3n + 24 = 3n - 12 + 36 = 3 (n -  4) + 36

Để 3n + 24 chia hết cho n-4 thì 36 chia hết cho n-4

=>n - 4EU (36) = {-36,-18,-12,-9,-6,-4,-3,-2,-1,1,2,3,4,6,9,12,18,36}

=> nE {-32, - 14 , - 8, - 5, - 2, 0 , 1, 2 , 3, 5 , 6, 7, 8, 10 ,13,16  , 22, 40}