引用:
原帖由 frombemask 於 2013-7-15 04:32 PM 發表 
正整數a,b,c,d滿足a+b=3(c+d), a+c=4(b+d), a+d=5(b+c), 求a可能的最小值。
令 b = md,c = nd (m 和 n 是有理數)
a = (-m + 3n + 3)d = (4m - n + 4)d = (5m + 5n - 1)d
-m + 3n + 3 = 4m - n + 4
4m - n + 4 = 5m + 5n - 1
m = 7/17,n = 13/17
b:c:d = 7:13:17
所求 = 3(13 + 17) - 7 = 83