解：y=(a-1)x+a与x轴、y轴的交点A、B坐标分别为A(-a/(a-1)，0)B(0，a)三角形OAB的面积 = |a * a/(a-1)|/2 = |a^2 / 2(a-1)|∵三角形OAB的面积是正整数，且a为整数∴可以设|a^2 / 2(a-1)| = k，其中k是正整数1）a＞1时a^2 / 2(a-1) = k整理得 a^2 - 2ka + 2k = 0(a - 1) (2k - 展开
解：y=(a-1)x+a与x轴、y轴的交点A、B坐标分别为A(-a/(a-1)，0)B(0，a)三角形OAB的面积 = |a * a/(a-1)|/2 = |a^2 / 2(a-1)|∵三角形OAB的面积是正整数，且a为整数∴可以设|a^2 / 2(a-1)| = k，其中k是正整数1）a＞1时a^2 / 2(a-1) = k整理得 a^2 - 2ka + 2k = 0(a - 1) (2k - a - 1) = 1因为k、a都是整数，所以a -1 = 1且 2k - a - 1 = 1或者a -1 = -1且 2k - a - 1 = -1解得a = 2或a = 0（舍去）2）a＜1时a^2 / 2(a-1) = -k整理得 a^2 - 2ka + 2k = 0(1 - a) (2k + a + 1) = 1因为k、a都是整数，所以1 - a = 1且 2k + a + 1 = 1或者1 - a = -1且 2k + a + 1 = -1解得a = 0（舍去）或a = 2所以a = 2 收起
