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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)

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Solution Solution | Comment 4 of 5 |
The three primes that meet the first condition are:
  • 11, 19, 43 --- 112+192+432 = 2331
  • 11, 23, 41 --- 112+232+412 = 2331
  • 11, 29, 37 --- 112+292+372 = 2331
  • 17, 19, 41 --- 172+192+412 = 2331
  • 23, 29, 31 --- 232+292+312 = 2331
Of these the only set of primes that meet the second condition is:
  • 11, 19, 43 --- 1+11+19+43+(11*19)+(11*43)+(19*43)+(11*19*43) = 10560
11*19*43 = 8987; N is therefore 8987
  Posted by Dej Mar on 2009-10-19 00:58:21
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