In this paper, we find all positive squarefree integers d such that the Pell equation X 2 − dY 2 = ±1 has at least two positive integer solutions (X, Y ) and (X , Y ) such that both X and X are sums of two Tribonacci numbers.

We find all positive integer solutions of the Diophantine equation F n + F m + F = 2 a , where F k is the kth term of the Fibonacci sequence. This paper continues and extends the previous work of J.J. Bravo and F. Luca [On the Diophantine equation F n + F m = 2 a , Quaest. Math., to appear]. MSC: 11B39, 11J86, 11D61

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