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 Figuring Forty-Nine and Sequence (Posted on 2016-10-25)
Find all possible triples (P, Q, R) of positive integers satisfying both of the following conditions

49, P2 and Q2 (in order) are in arithmetic sequence with common difference > 0 , and:

49, Q2 and R2 (in order) are in arithmetic sequence with common difference > 0

Prove that there are no others.

 No Solution Yet Submitted by K Sengupta No Rating

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 No proof, but ... | Comment 1 of 2
`                                   differences p  q  r     p^2 q^2 r^2      1st seq     2nd seq13 17 23     169 289 529      120 120     240 240`

any others would have p > 10,000,000

For p = 8 To 10000000
p2 = p * p
q2 = p2 + p2 - 49
sr = Int(Sqr(q2) + 0.5)
q = sr
If sr * sr = q2 Then
r2 = q2 + q2 - 49
sr = Int(Sqr(r2) + 0.5)
r = sr
If sr * sr = r2 Then
Text1.Text = Text1.Text & p & Str(q) & Str(r) & "     "
Text1.Text = Text1.Text & p2 & Str(q2) & Str(r2) & "     "
Text1.Text = Text1.Text & Str(p2 - 49) & Str(q2 - p2) & "    " & Str(q2 - 49) & Str(r2 - q2) & crlf
End If
End If
Next

 Posted by Charlie on 2016-10-25 09:18:28

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