Question

求方程（2x-1)(2y+5)=2009的正整数解

Answer 1

（2x-1)(2y+5)=2009=41*7*7=41*49=287*7=2009*1

2x-1=41

2y+5=49,x=21,y=22

2x-1=49

2y+5=41,x=25,y=18

2x-1=287

2y+5=7,x=144,y=1

2x-1=7

2y+5=287,x= 4,y=141

2x-1=1

2y+5=2009,x=1,y=1002