A positive integer X is defined as a bold number if precisely 8 of its distinct
divisors sum to 3240. The total number of divisors of X may or may not be equal to 8.
Determine the minimum positive bold number.
(In reply to
re: solution by Kenny M)
Much of my figuring was done with brute force, yet here is a little of the analysis:
As each number must be distinct, we can first find the least common denominator for the first 8 fractions:
1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, and 1/9
2,3,(2*2),5,(2*3),7,(2*2*2),(3*3) ::: 2^{3} * 3^{2} * 5 * 7 = 2520
With 2520 as the denominator for the 8 distinct divisors, this gives the numerator for 1/2 as 1260.
Edited on December 14, 2009, 1:46 am

Posted by Dej Mar
on 20091213 17:01:43 