a: \(n+12⋮n\)
=>\(12⋮n\)
mà n>=0
nên \(n\in\left\{1;2;3;4;6;12\right\}\)
b: \(15-4n⋮n\)
=>\(15⋮n\)
=>\(n\inƯ\left(15\right)\)
mà 0<=n<4
nên \(n\in\left\{1;3\right\}\)
c: \(n+13⋮n-5\)
=>\(n-5+18⋮n-5\)
=>\(n-5\in\left\{1;-1;2;-2;3;-3;6;-6;9;-9;18;-18\right\}\)
=>\(n\in\left\{6;4;7;3;8;2;11;-1;14;-4;23;-13\right\}\)
mà n>5
nên \(n\in\left\{6;7;8;11;14;23\right\}\)
d: \(-2n+15⋮n+1\)
=>\(-2n-2+17⋮n+1\)
=>\(n+1\inƯ\left(17\right)\)
=>\(n+1\in\left\{1;-1;17;-17\right\}\)
=>\(n\in\left\{0;-2;16;-18\right\}\)
mà 0<=n<=7
nên \(n=0\)
e: \(6n+9⋮4n-1\)
=>\(12n+18⋮4n-1\)
=>\(12n-3+21⋮4n-1\)
=>\(4n-1\in\left\{1;-1;3;-3;7;-7;21;-21\right\}\)
=>\(4n\in\left\{2;0;4;-2;8;-6;22;-20\right\}\)
=>\(n\in\left\{\dfrac{1}{2};0;1;-\dfrac{1}{2};2;-\dfrac{3}{2};\dfrac{11}{2};-5\right\}\)
mà n>=1 và n là số tự nhiên
nên \(n\in\left\{1;2\right\}\)