(In reply to
re: Some were discovered.... by Brian Smith)
I searched up to 2000 >= c >= b >=a >=1 and got only five more sets than Brian Smith: 92.
In each set, a never exceeds 25.
The stats are:
quotient # of occurrences
1 23
2 14
3 13
4 5
5 12
6 12
8 7
9 6
Interestingly, the first occurrences of the quotients appear in the order 9,8,6,5,4,3,2,1:
1 1 1 9
1 1 2 8
1 2 3 6
1 4 5 5
2 2 4 4
2 4 6 3
3 6 9 2
5 20 25 1
even though 1 is the most common quotient.
Dim quot(100)
Private Sub Command1_Click()
Open "natural numbers.txt" For Output As #2
For a = 1 To 2000
Text1.Text = Str(a)
For b = a To 2000
For c = b To 2000
DoEvents
q = (a + b + c) * (a + b + c) / (a * b * c)
If q = Int(q) Then
If quot(q) = 0 Then Print a, b, c, q
quot(q) = quot(q) + 1
Print #2, a, b, c, q
Text2.Text = Str(a)
Text3.Text = Str(b)
Text4.Text = Str(c)
Text5.Text = Str(q)
End If
Next
Next
Next
For i = 1 To 100
If quot(i) > 0 Then Print #2, i, quot(i)
Next
Close 2
Print "done"
End Sub
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Posted by Charlie
on 2007-10-15 14:19:53 |
re(2): Some were discovered....
