Linear forms in logarithms and the mathematical method of diophantine equations: applications in chemistry and physics

In this paper, we established the bound of n in term of p of the following equation F n = 2 p with n , p ≥ 0 where { F n } n ≥ 0 represent Fibonacci sequence defined by the following relation : F 0 = 0 , F 1 = 1 et F n + 1 = F n + F n - 1 for all n ≥ 1 . The method used here is the linear forms in logarithm introduced by the British mathematician Alan Baker in 1966 (Field medal 1970). We show in this paper, how to choose the parameters involving in the- determination of the bound of n in term of p and applications of mathematical method of Diophantine equations in Physics and Chemistry.