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1707 (Posted on 2012-08-23) Difficulty: 3 of 5
In how many distinct ways can 1707 be represented as a sum of 3 squares?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Computer derived | Comment 2 of 4 |
The program below 30 cases where the sum of 3 squares totalled 1707 but when that list was edited there were just 6 distinct cases as below:

Edited List
 1             1  1          5  25         41  1681
 4             5  25         29  841       29  841
 6             7  49         17  289       37  1369
 8             11  121       19  361       35  1225
 9             11  121       25  625       31  961
 12            13  169       13  169       37  1369


Generated List
 1             1  1          5  25         41  1681
 2             1  1          41  1681      5  25
 3             5  25         1  1          41  1681
 4             5  25         29  841       29  841
 5             5  25         41  1681      1  1
 6             7  49         17  289       37  1369
 7             7  49         37  1369      17  289
 8             11  121       19  361       35  1225
 9             11  121       25  625       31  961
 10            11  121       31  961       25  625
 11            11  121       35  1225      19  361
 12            13  169       13  169       37  1369
 13            13  169       37  1369      13  169
 14            17  289       7  49         37  1369
 15            17  289       37  1369      7  49
 16            19  361       11  121       35  1225
 17            19  361       35  1225      11  121
 18            25  625       11  121       31  961
 19            25  625       31  961       11  121
 20            29  841       5  25         29  841
 21            29  841       29  841       5  25
 22            31  961       11  121       25  625
 23            31  961       25  625       11  121
 24            35  1225      11  121       19  361
 25            35  1225      19  361       11  121
 26            37  1369      7  49         17  289
 27            37  1369      13  169       13  169
 28            37  1369      17  289       7  49
 29            41  1681      1  1          5  25
 30            41  1681      5  25         1  1

OPEN "c:qb64workx7.txt" FOR OUTPUT AS #1
count = 1
FOR a = 1 TO 41
 FOR b = 1 TO 41
  FOR c = 1 TO 41
   n = a ^ 2 + b ^ 2 + c ^ 2
   IF n = 1707 THEN
    PRINT count, a; a ^ 2, b; b ^ 2, c; c ^ 2
    PRINT #1, count, a; a ^ 2, b; b ^ 2, c; c ^ 2
    count = count + 1
   END IF
  NEXT
 NEXT
NEXT

CLOSE 1

Edited on August 24, 2012, 9:08 am
  Posted by brianjn on 2012-08-23 20:07:47

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