Question

5x-3y=4的正整数解,

Answer 1

y=(5x-4)/3=(x-1)+(2x-1)/3
令2x-1=3n
x=(3n+1)/2=n+(n+1)/2
要x为正整数,n>=1,且为奇数.令n=2m-1(m=1,2,...)
x=2m-1+m=3m-1
y=(3m-1-1)+2m-1=5m-3
因此,本题有无数组（x,y)正整数解组.但需要满足：
x=3m-1
y=5m-3
(m=1,2,3.)