 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Arithmetic Numbers Enumeration (Posted on 2014-12-19) Consider five positive integers A < B < C < D < E in arithmetic sequence, and find all possible solutions of:
A4 + B4 + C4 + D4 = E4 - 143

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution | Comment 1 of 2

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

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For a = 1 To 10000
For diff = 1 To 10000
d = a + 3 * diff
d4 = d * d * d * d
If d4 > 1E+15 Then Exit For
b = a + diff: c = b + diff
tot = a * a * a * a + b * b * b * b + c * c * c * c + d4
totPlus = tot + 143
rt = Int(Sqr(Sqr(totPlus)) + 0.5)
If rt * rt * rt * rt = totPlus Then
Text1.Text = Text1.Text & a & Str(diff) & crlf
DoEvents
End If
Next
Next a

Text1.Text = Text1.Text & " done"
End Sub

Finds only A = 3 and the successive differences are 1:

3^4 + 4^4 + 5^4 + 6^4 = 7^4 - 143

The program negelected to check that E was part of the arithmetic sequence, but the only sequence found for A through D did indeed result in an E that was part of the sequence.

 Posted by Charlie on 2014-12-19 15:29:55 Please log in:

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