prep-2-80求思路~~

80.  7589-!-item-!-187;#058&005492

If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ?

(1) x = 12u, where u is an integer.

(2) y = 12z, where z is an integer.

怎么判断1）不是呢？

多谢不吝赐教啊~

1) x=36 y=3     x=60 y=6    这就把1给否了

If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ?

(1) x = 12u, where u is an integer. ——将此条代入原式之中，得到12u=8y+12 ，整理得到以下两个式子

     x=12u, y=(u-1)*4/3

     可以发现，u=4,7,10....时，x与y的最大公约数在不断增加，即无解

(2) y = 12z, where z is an integer. 类似处理，得到

     x=12*(8z+1), y=12z

     由于z为正数，8z+1与z必然不想等，则最大公约数只能是12——得解

给楼上两位献花了！！~