以知正整数a、b、c、d满足条件a/b=b/c=c/d=5/8,求a+b+c+d的最小值

由已知：a/b=b/c=c/d=5/8所以,a < b < c < d先看c/d=5/8,可设c =5m,d =8m（m为正整数）由b/c =5/8,可知：b =25m/8,所以,m应该是8的整数倍。由a/b =5/8,可知：a = 25b/8 =625m/64,所以,m应该是64的整数倍。所以,a+b+c+d= 625m/64 +25m/8 +8m +5m = 1157m/64显然,当m =64时,a+b+c+d值最小,为1157。