若x, y∈z且3x+2y=xy,則(x, y)之整數解有幾組?

若x，y∈z且3x+2y=xy，則(x，y)之整數解有幾組?
Sol
3x+2y=xy
3x－xy+2y=0
x(3－y)－2(－y)=0
x(3－y)－2(3－y)=－6
(x－2)(y－3)=6
6=(2^1)*(3^1)
有(1+1)*(1+1)=4個正因數
(x，y)之整數解有8組