这样吧：
DeleteCases[
Table[If[FindInstance[
2 x1 + 3 x2 + 4 x3 == 20 && 5 x1 + 6 x2 + 7 x3 + 1 == m*y &&
0 < x1 < 13 && 0 < x2 < 30 && 0 < x3 < 30,{x1,x2,x3,y},
Integers] == {},m],{m,6,14}],Null]
Wolfram Mathematica 如何用枚举搜索方程无解
这样吧：
DeleteCases[
Table[If[FindInstance[
2 x1 + 3 x2 + 4 x3 == 20 && 5 x1 + 6 x2 + 7 x3 + 1 == m*y &&
0 < x1 < 13 && 0 < x2 < 30 && 0 < x3 < 30,{x1,x2,x3,y},
Integers] == {},m],{m,6,14}],Null]