perplexus.info :: Numbers : Four integers

Four integers (Posted on 2016-12-04)

Find four distinct positive integers such that:
a. Each of them is below 500.
b. Multiplying any two of them and then incrementing the product by 1
produces a square number.

No Solution Yet Submitted by Ady TZIDON

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computer solution (spoiler)

| Comment 1 of 8

DefDbl A-Z

Dim crlf$, n(4)

Private Sub Form_Load()

Form1.Visible = True

Text1.Text = ""

crlf = Chr$(13) + Chr$(10)

For a = 1 To 496

n(1) = a

addOn 2

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

End Sub

Sub addOn(wh)

For newNum = n(wh - 1) + 1 To 499

n(wh) = newNum

good = 1

For i = 1 To wh - 1

For j = i + 1 To wh

DoEvents

sq = n(i) * n(j) + 1

sr = Int(Sqr(sq) + 0.5)

If sr * sr <> sq Then good = 0: Exit For

If good = 0 Then Exit For

If good Then

If wh = 4 Then

For i = 1 To 4

Text1.Text = Text1.Text & Str(n(i))

Text1.Text = Text1.Text & crlf

Else

addOn wh + 1

End If

End Sub

finds these two solutions:

1 3 8 120

2 4 12 420

Posted by Charlie on 2016-12-04 11:01:08

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