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 2*P + 2 = Perfect Square? (Posted on 2010-05-01)
Each of P and Q is a nonnegative integer satisfying the equation: P2 = 28*Q2 + 1

Is 2*P + 2 always a perfect square?

If so, prove it. Otherwise, provide a counterexample.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 a computerized start but no proof and too small a sample size | Comment 1 of 5
`list   10   for Q=0 to 10000000   20   P2=28*Q*Q+1   30   P=int(sqrt(P2)+0.5)   40   if P*P=P2 then   50     :Perfsq=2*P+2   60     :Sr=sqrt(Perfsq)   70     :print Q;P,Perfsq;Sr   80   nextOK`
` Q        P         2P+2      Sqrt(2P+2) 0        1         4         2.0 24       127       256       16.0 6096     32257     64516     254.0 1548360  8193151   16386304  4048.0`

Every entry in column 3 is a perfect square, giving some credibility to the assertion, but not even a statistical proof.

 Posted by Charlie on 2010-05-01 16:12:05

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