We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
320
2
avatar+363 

The product of the proper positive integer factors of n can be written as n^[(ax+b)/c], where x is the number of positive divisors n has, c is a positive integer, and the greatest common factor of the three integers a, b, and c is 1. What is a+b+c?

 Nov 2, 2018
 #1
avatar
0

n =110 = 2 x 5 x 11
a=2, b=5, c=11
110^((3*2 + 5)/11)=110^(11/11)=110
GCD [2, 5, 11] =1
a + b + c =2 + 5 + 11 = 18

Note: With 2 as the first factor, many n will meet the restrictions given in the question.

Examples: 2, 7, 13 =182,  2, 11, 17 =374,  2, 13, 19 =494,   2, 17, 23 =782,  2, 23, 29 =1,334......etc.

 Nov 2, 2018
edited by Guest  Nov 2, 2018
 #2
avatar
0

I don't think you understood the question, a b and c don't have to be factors of n, and x is the number of proper positive factors of n, not the number of prime factors of n.

Guest Nov 2, 2018

24 Online Users