Let n be number of lines intersecting 1x+2y−3z=1  in first octant at infinite integral points, and m be number of integral points in first octant not lying on these lines then n+m is

Let 1x=a1y=b,1z=c then a+2b−3c=1 where 2b=1+3c−a the a,b,c≤1 Make cases for a=1,12 get (1,2n,3n)(2,1;2) for a≤132b>23⇒b>13 orb =1,b=2 make those two cases. x=1,y2=z3;y=2,z=3x and two extra cases (2,1,2),(2,3,18)