It is known that there are only finitely many perfect powers in non degenerate binary recurrence sequences. However explicitly finding them is an interesting and a difficult problem for binary recurrence sequences. A recent breakthrough result of Bugeaud, Mignotte and Siksek states that Fibonacci sequences (F_n) given by F_0 = 0; F_1 = 1 and F_{n+2} = F_{n+1} + F_n for n >= 0 are perfect powers only for F_0 = 0; F_1 = 1; F_2 = 1; F_6 = 8 and F_12 = 144.

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Last updated: 06 Mar 2020