@article { author = {Tiebekabe, P. and Diouf, I.}, title = {On solutions of the Diophantine equation $F_{n_{1}}+F_{n_{2}}+F_{n_{3}}+F_{n_{4}}=2^a$}, journal = {Journal of Algebra and Related Topics}, volume = {9}, number = {2}, pages = {131-148}, year = {2021}, publisher = {University of Guilan}, issn = {2345-3931}, eissn = {2382-9877}, doi = {10.22124/jart.2021.19294.1266}, abstract = {Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by $F_0 = 0, F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for $n \geq 0$. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize.}, keywords = {Linear forms in logarithm,Diophantine equations,Fibonacci sequence,Lucas sequence,perfect powers}, url = {https://jart.guilan.ac.ir/article_5322.html}, eprint = {https://jart.guilan.ac.ir/article_5322_4dbb7688267f38276f282624efaf9151.pdf} }