三个不同质数a、b、c满足abc+a=200,求a+b+c的值

Question

三个不同质数a、b、c满足abc+a=200,求a+b+c的值

Answer 1

200 = 2*2*2*5*5,因abc+a=200,所以a整除200,又a是质数,所以a = 2或a = 5.
1)若a = 2,则bc + 1 = 100,即bc = 99 = 3 * 3 * 11,而b,c 均为质数,此式无解
2）若a = 5,则bc + 1 = 40,bc = 39 = 3 * 13,又b,c 均为质数,所以b = 3 ,c = 13 或b = 13,c = 3,
总之a+b+c = 5 + 3 +13 = 21