PREP2-DS-60

shuangyuym

Does the integer k have a factor p such that 1 < p < k ?

 

(1) k > 4!

 

(2) 13! + 2 <= K <= 13! + 13

 

答案(B), 求教~谢谢!!

 

nickynicky

 (1)k > 4!= 24  if k =29, a prime number, then k has no factor between 1 and itself
(2)13! = 1*2*3*...*13. so if k is an interger between 13! +2 and 13!+13, inclusive, k definitely has a product smaller than k. i.e. k = 13!+5 = 5 * (1*2*3*4*6*...*13+1) so k has a factor 5 such that 1<5<k

shuangyuym

got it. thanks so much.