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

 Three Prime Product (Posted on 2009-10-18)
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.)
 computer solution | Comment 3 of 5 |

The first criterion is satisfied by the following:

`--primes--      N11  19  43      898711  23  41      1037311  29  37      1180317  19  41      1324323  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   61462  31  109   67582  43  79    67943  5   439   65853  19  131   74673  23  109   75213  43  59    76117  11  109   83937  29  43    872911 19  43    8987`

 Posted by Charlie on 2009-10-18 15:38:15

 Search: Search body:
Forums (0)