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.

(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
P^2-28Q^2=1
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