Question

a) Tìm số nguyên a biết 17 chia hết cho ( 2a + 3 )
b) Tìm số nguyên n , sao cho : ( n - 6 ) chia hết ( n - 1 )

Answer 1

a) \(17⋮2a+3\)

\(\Leftrightarrow2a+3\inƯ\left(17\right)=\left\{1,-1,17,-17\right\}\)

\(\Leftrightarrow2a=-2,-4,14,-20\)

\(\Leftrightarrow a=-1,-2,7,-10\)

b)\(\left(n-6\right)⋮\left(n-1\right)\)

\(Ta\)\(có\): n-6 = n-1-5

Vì \(\left(n-1\right)⋮\left(n-1\right)\)nên để\(\left(n-6\right)⋮\left(n-1\right)thì5⋮n-1\)

\(\Leftrightarrow n-1\inƯ\left(5\right)=\left\{1,-1,5,-5\right\}\)

\(\Leftrightarrow n=2,0,6,-4\)