Abstract
Let d ge 2 be an integer which is not a square. We show that if (F_n)_{nge 0} is the Fibonacci sequence and (X_m, Y_m)_{mge 1} is the mth solution of the Pell equation X^2 -dY^2 = pm 1, then the equation Y_m = F_n has at most two positive integer solutions (m, n) except for d=2 when it has three solutions (m,n)=(1,2),(2,3),(3,5).
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