Question

x,y都是非零自然数,解下面的不定方程:8x+11y=106 1/3x+1/4y=9/4

Answer 1

8x + 11y = 106

首先y是偶数,设y=2n

则 4x + 11n = 53

n是奇数,n只能为1或3

经验证n=3时有整数解

解为x = 5 ,y = 6

4x + 3y = 27

则x是3的倍数,设x=3k

4k + y = 9

则y是奇数,y=5或1

所以解为x = 3,y = 5或x = 6,y = 1