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2*P + 2 = Perfect Square? (Posted on 2010-05-01) Difficulty: 4 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): a computerized start but no proof and too small a sample size | Comment 4 of 5 |
(In reply to re: a computerized start but no proof and too small a sample size by Jer)

P^2=28Q^2+1 is a pell equation when put in the form
and there are established methods for finding all solutions to these types of equations (just google pell equation).  In fact the method of solution is to find a recurrence relation like you did.  So it is fairly easy to establish that your recurrence denotes all of the solutions.  The hard part is the inductive proof which I as well have been attempting with no success
  Posted by Daniel on 2010-05-03 10:31:08

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