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Please, help me to determine the set A={x integer/x=(6n-7)/(2n+1), n integer}. Thank you!

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Please, help me to determine the set A={x integer/x=(6n-7)/(2n+1), n integer}. Thank you!

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In order to find out the elements of the set A, we have to notice that the property of the set is that all it's elements are integer numbers (x integer).

For x to be integer, (2n+1) has to be the divisor of the

(6n-7).

(6n-7)=3(2n+1)-10

If we divide the expression above, with (2n+1), the result will be:

(6n-7)/(2n+1)=3-10/(2n+1)

But x=(6n-7)/(2n+1) and x integer, so, in order to obtain x integer, (2n+1) has to be a divisor of 10.

D10=+/-2;+/-5;+/-1;+/-10

(2n+1)=1, 2n=0, n=0, x=(6*0-7)/(2*0+1)=-7/1=-7

(2n+1)=-1,2n=-2,n=-1, x=(6*(-1)-7)/(2*(-1)+1)=13

(2n+1)=2, 2n=1, n=1/2 not integer

(2n+1)=-2, 2n=-3, n=-3/2 not integer

(2n+1)=5, 2n=4, n=2,x=(6*(2)-7)/(2*(2)+1)=5/5=1

(2n+1)=-5, 2n=-6, n=-3, x=(6*(-3)-7)/(2*(-3)+1)=5

(2n+1)=10, 2n=9, n=9/2 not integer

(2n+1)=-10, 2n=-11, n=-11/2 not integer

A={-7,1,5,13}

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