a: \(n-14⋮n+3\)
=>\(n+3-17⋮n+3\)
=>\(-17⋮n+3\)
=>\(n+3\in\left\{1;-1;17;-17\right\}\)
=>\(n\in\left\{-2;-4;14;-20\right\}\)
b: \(4n+7⋮2n+1\)
=>\(4n+2+5⋮2n+1\)
=>\(5⋮2n+1\)
=>\(2n+1\inƯ\left(5\right)\)
=>\(2n+1\in\left\{1;-1;5;-5\right\}\)
=>\(2n\in\left\{0;-2;4;-6\right\}\)
=>\(n\in\left\{0;-1;2;-3\right\}\)
c: \(2n-5⋮3n+4\)
=>\(6n-15⋮3n+4\)
=>\(6n+8-23⋮3n+4\)
=>\(-23⋮3n+4\)
=>\(3n+4\in\left\{1;-1;23;-23\right\}\)
=>\(3n\in\left\{-3;-5;19;-27\right\}\)
=>\(n\in\left\{-1;-\dfrac{5}{3};\dfrac{19}{3};-9\right\}\)
mà n nguyên
nên \(n\in\left\{-1;-9\right\}\)
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