<s>[INST] Find all positive integers solution of $xy+yz+xz = xyz+2$ 1.Find all positive  integers solution
$xy+yz+xz = xyz+2$
2.Determine all p and q which p,q are prime number and satisfy
$p^3-q^5 = (p+q)^2$
Thx for the answer
3.Find all both positive or negative integers that satisfy
$\frac{13}{x^2} + \frac{1996}{y^2} = \frac{z}{1997}$
 [/INST] 1.set $x≤y≤z,xyz<xyz+2=xy+yz+zx≤3yz,$
so $0<x<3,x=1,2$
If $x=1,y+z+yz=yz+2,y+z=2$,so $x=y=z=1$
If $x=2,2y+2z+yz=2yz+2,yz=2y+2z-2<4z,2≤y<4,y=3,z=4$
so the only solution to the fisrt equation is $x=y=z=1$ or $x=2,y=3,z=4$ or change their order.
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