DefDbl A-Z
Dim crlf$
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
ChDir "\VB5 projects\flooble"
For goal = 3 To 50000
For b2 = 2 To goal - 1 Step 2
b = b2 / 2: a = goal - b2
sr1 = Int(Sqr(goal) + 0.5)
If sr1 * sr1 = goal Then
If gcd(a, b) = 1 Then
f2 = a * a + b2 * b
sr = Int(Sqr(f2) + 0.5)
If sr * sr = f2 Then
Text1.Text = Text1.Text & mform(a, "######0") & mform(b, "#####0") & " " & mform(f2, "###########0") & mform(goal, "#######0")
Text1.Text = Text1.Text & " " & mform(sr, "######0") & mform(sr1, "#####0") & crlf
DoEvents
End If
End If
End If
Next
Next
Text1.Text = Text1.Text & "done"
DoEvents
End Sub
Function gcd(a, b)
x = a: y = b
Do
q = Int(x / y)
z = x - q * y
x = y: y = z
Loop Until z = 0
gcd = x
End Function
finds the 21 smallest such values with 24 cases of A and B, as 3 values of A + 2*B can result from two different pairs (A,B) each:
respective
A B A^2 + 2*B^2 A + 2*B square roots
1 12 289 25 17 5
257 136 103041 529 321 23
217 204 130321 625 361 25
233 304 239121 841 489 29
337 756 1256641 1849 1121 43
889 660 1661521 2209 1289 47
1777 516 3690241 2809 1921 53
1049 1720 7017201 4489 2649 67
3049 1140 11895601 5329 3449 73
6433 1296 44742721 9025 6689 95
4937 2044 32729841 9025 5721 95
5921 3652 61732449 13225 7857 115
9289 3168 106357969 15625 10313 125
8233 5544 129254161 19321 11369 139
14249 3388 225991089 21025 15033 145
2513 9256 177662241 21025 13329 145
16961 2620 301404321 22201 17361 149
13777 6396 271623361 26569 16481 163
4249 12840 347785201 29929 18649 173
7441 14520 477029281 36481 21841 191
25769 6520 749062161 38809 27369 197
6793 18864 757845841 44521 27529 211
36961 4632 1409026369 46225 37537 215
10057 18084 755205361 46225 27481 215
Only values of A + 2*B up to 50,000 were computed.
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Posted by Charlie
on 2015-03-15 12:52:08 |
computer solution
