Question

求不定方程x+2+y+3+z=18的非负整数解的组数

Answer 1

问：求不定方程x+2+y+3+z=18的非负整数解的组数

问：可以帮我把过程写下吗？

问：这题也可以帮我看一下吗？

答：求不定方程x+2+y+3+z=18的非负整数解的组数不是问这个吗？

问：你的题目错了，是x+2 y+3 z=18

答：求不定方程x+2y+3z=18的非负整数解的组数非负整数解的组数有19个

问：麻烦快点，还没好吗？，请帮我把步骤都写一下，不要只有答案就行

答：x=1, y=1 =>z=5          ; (x,y,z) = (1,1,5)x=1, y=2 =>z=13/3        ( 舍去)x=1, y=3 =>z=11/3        ( 舍去)x=1, y=4 =>z=3        ; (x,y,z) = (1,4,3)x=1, y=5 =>z=7/3        ( 舍去)x=1, y=6 =>z=5/3        ( 舍去)x=1, y=7 =>z=1           ; (x,y,z) = (1,7,1)x=2, y=1 =>z=14/3        ( 舍去)x=2, y=2 =>z=4         ; (x,y,z) = (2,2,4)x=2, y=3 =>z=10/3        ( 舍去)x=2, y=4 =>z=8/3        ( 舍去)x=2, y=5 =>z=2         ; (x,y,z) = (2,5,2)x=2, y=6 =>z=4/3       ( 舍去)x=2, y=7 =>z=2/3       ( 舍去)

答：x=3, y=1 =>z=13/3 ( 舍去)x=3, y=2 =>z=11/3 ( 舍去)x=3, y=3 =>z=3 ; (x,y,z) = (3,3,3)x=3, y=4 =>z=7/3 ( 舍去)x=3, y=5 =>z=5/3 ( 舍去)x=3, y=6 =>z=1 ; (x,y,z) = (3,6,1)x=4, y=1 =>z=4 ; (x,y,z) = (4,1,4)x=4, y=2 =>z=10/3 ( 舍去)x=4, y=3 =>z=8/3 ( 舍去)x=4, y=4 =>z=2 ; (x,y,z) = (4,4,2)x=4, y=5 =>z=4/3 ( 舍去)x=4, y=6 =>z=2/3 ( 舍去)x=5, y=1 =>z=11/3 ( 舍去)x=5, y=2 =>z=3 ; (x,y,z) = (5,2,3)

答：x=3, y=5 =>z=5/3 ( 舍去)x=3, y=6 =>z=1 ; (x,y,z) = (3,6,1)x=4, y=1 =>z=4 ; (x,y,z) = (4,1,4)x=4, y=2 =>z=10/3 ( 舍去)x=4, y=3 =>z=8/3 ( 舍去)x=4, y=4 =>z=2 ; (x,y,z) = (4,4,2)x=4, y=5 =>z=4/3 ( 舍去)x=4, y=6 =>z=2/3 ( 舍去)x=5, y=1 =>z=11/3 ( 舍去)x=5, y=2 =>z=3 ; (x,y,z) = (5,2,3)x=5, y=3 =>z=7/3 ( 舍去)x=5, y=4 =>z=5/3 ( 舍去)x=5, y=5 =>z=1 ; (x,y,z) = (5,5,1)x=6, y=1 =>z=10/3 ( 舍去)

答：x=6, y=2 =>z=8/3       ( 舍去)x=6, y=3 =>z=2       ; (x,y,z) = (6,3,1)x=6, y=4 =>z=4/3       ( 舍去)x=6, y=5 =>z=2/3       ( 舍去)x=7, y=1 =>z=3       ; (x,y,z) = (7,1,3)x=7, y=2 =>z=7/3       ( 舍去)x=7, y=3 =>z=5/3       ( 舍去)x=7, y=4 =>z=1       ; (x,y,z) = (7,4,1)x=8, y=1 =>z=8/3       ( 舍去)x=8, y=2 =>z=2       ; (x,y,z) = (8,2,2)x=8, y=3 =>z=4/3       ( 舍去)x=8, y=4 =>z=2/3       ( 舍去)x=9, y=1 =>z=7/3       ( 舍去)x=9, y=2 =>z=5/3       ( 舍去)x=9, y=3 =>z=1       ; (x,y,z) = (9,3,1)x=10,

答：x=10, y=1 =>z=2 ; (x,y,z) = (10,1,2)x=10, y=2 =>z=4/3 ( 舍去)x=10, y=3 =>z=2/3 ( 舍去)x=11, y=1 =>z=5/3 ( 舍去)x=11, y=2 =>z=1 ; (x,y,z) = (11,2,1)x=12, y=1 =>z=4/3 ( 舍去)x=12, y=2 =>z=2/3 ( 舍去)x=13, y=1 =>z=1 ; (x,y,z) = (13,1,1)