 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Expression Quotient Puzzle (Posted on 2015-06-16) Find all pairs (x,y) of positive integers x and y such that:
x + y + 1 divides 2xy and:
x + y − 1 divides x2 + y2 − 1

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: Some, maybe all | Comment 2 of 3 | (In reply to Some, maybe all by Jer)

Checking for all x and y whose sum is under 46000, assures there are no sporadic cases among those.  (The total was set to go higher, but met overflow around 46,000).

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For tot = 2 To 100000
For x = 1 To tot / 2
y = tot - x
If Abs(x - y) <> 1 Then
sm = tot + 1: prd = 2 * x * y
If prd Mod sm = 0 Then
df = tot - 1: sq = x * x + y * y - 1
If sq Mod df = 0 Then
Text1.Text = Text1.Text & x & Str(y) & crlf
DoEvents
End If
End If
End If
Next
Next

Text1.Text = Text1.Text & mxn & crlf & " done"

End Sub

 Posted by Charlie on 2015-06-16 12:08:54 Please log in:

 Search: Search body:
Forums (2)