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For an integer d ≥ 2 which is not a square, we show that there is at most one value of the positive integer x participating in the Pell equation x 2 − dy 2 = ±4 which is a Fibonacci number, except when d = 2, 5, cases in which we have exactly two values of x being members of the Fibonacci sequence.

For an integer d ≥ 2 which is not a square, we show that there is at most one value of the positive integer X participating in the Pell equation X 2 − dY 2 = ±1 which is a Lucas number, with a few exceptions that we completely characterize.

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No abstract