The set of integers {x,y,z} complies with the following set of equations:

**
x+y+xy=17 **

x+z+xz=35

y+z+yz=71

**
** Evaluate {x,y,z}.

(x+1)(y+1) = 18

(y+1)(z+1) = 36

(z +1)(x+1) = 72

Taking (A, B, C)= (x+1, y+1, z+1)

We have: AB =18, BC = 36, and CA =72

Thus, multiplying the three equations together, we have:

A^2*B^2*C^2 = 18*36*72 = 18^2* 2*72 = 18^2*12^2

=> ABC = 18*12 = 216

=> A = 216/36 =6 => x+1 =6 => x =5

B = 216/72 =3 => y +1 =3 => y =2

C = 216/18 = 12 = > z= 12-1 =11

Consequently, (x,y,z) = (5,2,11) comprises the only solution set corresponding to the given set of equations.