2(a+2ab+b)=1994 4ab+2a+2b=1994 4ab+2a+2b+1=1995 (2a+1)(2b+1)=1995 又a,b為正整數,所以(2a+1),(2b+1)為正整數 故(2a+1,2b+1)=(1,1995),(3,665),(5,399),(7,285),(15,133),(19,105),(21,95),(35,57),(57,35),(95,21),(105,19),(133,15),(285,7),(399,5),(665,3),(1995,1) 所以(a,b)=(0,997),(1,332),(2,199),(3,143),(7,66),(9,52),(10,47),(17,28),(28,17),(47,10),(52,9),(66,7),(143,3),(199,2),(332,1),(997,0) 又(0,997),(997,0)不合, 所以答案為(1,332),(2,199),(3,143),(7,66),(9,52),(10,47),(17,28),(28,17),(47,10),(52,9),(66,7),(143,3),(199,2),(332,1) |