All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Three Prime Product (Posted on 2009-10-18) Difficulty: 2 of 5
Determine all possible value(s) of a positive integer N that satisfies the following conditions:

(i) N is the product of three prime numbers, whose squares sum to 2331.

(ii) The sum of the positive divisors of N ( including 1 and N) is 10560.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 3 of 5 |

The first criterion is satisfied by the following:

--primes--      N
11  19  43      8987
11  23  41      10373
11  29  37      11803
17  19  41      13243
23  29  31      20677

Of these, only the first also satisfies the second criterion.

So the only answer is N = 8987.

   10   for N1=1 to 15
   20   for N2=N1+1 to 15
   30   for N3=N2+1 to 15
   40    P1=prm(N1):P2=prm(N2):P3=prm(N3)
   50    Ts=P1*P1+P2*P2+P3*P3
   60    if Ts=2331 then
   70       :print P1;P2;P3,P1*P2*P3
   80       :Sd=1+P1+P2+P3+P1*P2+P1*P3+P2*P3+P1*P2*P3
   90       :if Sd=10560 then print "   ";P1;P2;P3,P1*P2*P3
  200   next
  210   next
  220   next
 

BTW, within the range checked (highest prime is 47, so its square doesn't exceed 2331), the only other N to satisfy the second criterion is 8729 ( = 7 * 29 * 43).  And a complete list of numbers that satisfy the second criterion is:

2  7   439   6146
2  31  109   6758
2  43  79    6794
3  5   439   6585
3  19  131   7467
3  23  109   7521
3  43  59    7611
7  11  109   8393
7  29  43    8729
11 19  43    8987

  Posted by Charlie on 2009-10-18 15:38:15
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information